BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Alberto Elduque (University of Zaragoza\, Spain)
DTSTART:20230109T150000Z
DTEND:20230109T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/1
DESCRIPTION:Title: Tensor categories\, algebras\, and superalgebras\nby Alberto Eldu
que (University of Zaragoza\, Spain) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nAfter reviewing the basic definitions of ten
sor categories and the notion of semisimplification of symmetric tensor ca
tegories\, it will be shown how the semisimplification of the category of
representations of the cyclic group of order 3 over a field of characteris
tic 3 is naturally equivalent to the category of vector superspaces over t
his field. This allows to define a superalgebra starting with any algebra
endowed with an order 3 automorphism. As a noteworthy example\, the except
ional composition superalgebras will be obtained\, in a systematic way\, f
rom the split octonion algebra.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seidon Alsaody (Uppsala University\, Sweden)
DTSTART:20230116T150000Z
DTEND:20230116T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/2
DESCRIPTION:Title: Brown algebras\, Freudenthal triple systems and exceptional groups ov
er rings\nby Seidon Alsaody (Uppsala University\, Sweden) as part of E
uropean Non-Associative Algebra Seminar\n\n\nAbstract\nExceptional algebra
ic groups are intimately related to various classes of non-associative alg
ebras: for example\, octonion algebras are related to groups of type $G_2$
and $D_4$\, and Albert algebras to groups of type $F_4$ and $E_6$. This c
an be used\, on the one hand\, to give concrete descriptions of homogeneou
s spaces under these groups and\, on the other hand\, to parametrize isoto
pes of these algebras using said homogeneous spaces. The key tools are pro
vided by the machinery of torsors and faithfully flat descent\, working ov
er arbitrary commutative rings (sometimes assuming 2 and 3 to be invertibl
e).\n\nI will talk about recent work where we do this from Brown algebras
and their associated Freudenthal triple systems\, whose automorphism group
s are of type $E_6$ and $E_7$\, respectively. I will hopefully be able to
show how algebraic and geometric properties come together in this picture.
\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karel Dekimpe (Catholic University of Leuven\, Belgium)
DTSTART:20230123T150000Z
DTEND:20230123T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/3
DESCRIPTION:Title: Di-semisimple Lie algebras and applications in post-Lie algebra struc
tures\nby Karel Dekimpe (Catholic University of Leuven\, Belgium) as p
art of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe call a L
ie algebra $\\mathfrak g$ di-semisimple if it can be written as a vector s
pace sum $\\mathfrak g = \\mathfrak s_1 + \\mathfrak s_2$\, where $\\mathf
rak s_1$ and $\\mathfrak s_2$ are semisimple subalgebras of $\\mathfrak g$
and we say that $\\mathfrak g$ is strongly di-semisimple if $\\mathfrak
g$ can be written as a direct vector space sum of semisimple subalgebras.
We will show that complex strongly di-semisimple Lie algebras have to be s
emisimple themselves. \n\nWe will then use this result to show that if a p
air of complex Lie algebras $(\\mathfrak g\, \\mathfrak n)$ with $\\mathfr
ak g$ semisimple admits a so called post-Lie algebra structure\, then \n$\
\mathfrak n$ must be isomorphic to $\\mathfrak g$. \n\nJoint work with Die
trich Burde and Mina Monadjem.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Towers (Lancaster University\, UK)
DTSTART:20230130T150000Z
DTEND:20230130T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/4
DESCRIPTION:Title: Zinbiel algebras are nilpotent\nby David Towers (Lancaster Univer
sity\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstra
ct\nZinbiel algebras were introduced by Loday in 1995. They are the Koszul
dual of Leibniz algebras and Lemaire proposed the name of Zinbiel\, which
is obtained by writing Leibniz backwards. In this talk\, I will introduce
some of their main properties\, including the fact that\, over any field\
, they are nilpotent.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Franchi (Catholic University of the Sacred Heart\, Italy)
DTSTART:20230206T150000Z
DTEND:20230206T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/5
DESCRIPTION:Title: Axial algebras of Monster type\nby Clara Franchi (Catholic Univer
sity of the Sacred Heart\, Italy) as part of European Non-Associative Alge
bra Seminar\n\n\nAbstract\nExtending earlier work by Ivanov on Majorana al
gebras\, axial algebras of Monster type were introduced in 2015 by Hall\,
Rehren and Shpectorov in order to axiomatise some key features of certain
classes of algebras related to large families of finite simple groups\, su
ch as the weight-2 components of OZ-type vertex operator algebras\, Jordan
algebras\, and Matsuo algebras. In this talk\, I'll review the definition
of axial algebras and the major examples. Then I'll discuss the general c
lassification problem of the 2-generated objects and\, time permitting\, s
how its applications in some special cases related to the Monster.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin McInroy (University of Chester\, UK)
DTSTART:20230213T150000Z
DTEND:20230213T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/6
DESCRIPTION:Title: Classifying quotients of the Highwater algebra\nby Justin McInroy
(University of Chester\, UK) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nAxial algebras are a class of non-associative algeb
ras with a strong natural link to groups and have recently received much a
ttention. They are generated by axes which are semisimple idempotents who
se eigenvectors multiply according to a so-called fusion law. Of primary
interest are the axial algebras with the Monster type $(\\alpha\, \\beta)$
fusion law\, of which the Griess algebra (with the Monster as its automor
phism group) is an important motivating example.\n\nBy previous work of Ya
be\, and Franchi and Mainardis\, any symmetric 2-generated axial algebra o
f Monster type $(\\alpha\, \\beta)$ is either in one of several explicitly
known families\, or is a quotient of the infinite-dimensional Highwater a
lgebra $\\mathcal{H}$\, or its characteristic 5 cover $\\hat{\\mathcal{H}}
$. We complete this classification by explicitly describing the infinitel
y many ideals and thus quotients of the Highwater algebra (and its cover).
As a consequence\, we find that there exist 2-generated algebras of Mons
ter type $(\\alpha\, \\beta)$ with any number of axes (rather than just $1
\, 2\, 3\, 4\, 5\, 6\, \\infty$ as we knew before) and of arbitrarily larg
e finite dimension.\n\n\nIn this talk\, we will begin with a reminder of a
xial algebras which were introduced last week.\n\n\nThis is joint work wit
h:\nClara Franchi\, Catholic University of the Sacred Heart\, Milan\nMario
Mainardis\, University of Udine\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Iohara (University of Lyon\, France)
DTSTART:20230220T150000Z
DTEND:20230220T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/7
DESCRIPTION:Title: On Elliptic Root Systems\nby Kenji Iohara (University of Lyon\, F
rance) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\n
In 1985\, K. Saito introduced elliptic root systems as root systems belong
ing to a real vector space $F$ equiped with a symmetric bilinear form $I$
with signature $(l\, 2\, 0)$. Such root systems are studied in view of sim
ply elliptic singularities which are surface singularities with a regular
elliptic curve in its resolution. K. Saito had classified elliptic root sy
stems $R$ with its one dimensional subspace $G$ of the radical of $I$\, in
the case when $R/G \\subset F/G$ is a reduced affine root system. In our
joint work with A. Fialowski and Y. Saito\, we have completed its classifi
cation\; we classified the pair $(R\,G)$ whose quotient $R/G \\subset F/G$
is a non-reduced affine root system. In this talk\, we give an overview o
f elliptic root sysems and describe some of the new root systems we have f
ound.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dietrich Burde (University of Vienna\, Austria)
DTSTART:20230227T150000Z
DTEND:20230227T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/8
DESCRIPTION:Title: Pre-Lie algebra structures on reductive Lie algebras and etale affine
representations\nby Dietrich Burde (University of Vienna\, Austria) a
s part of European Non-Associative Algebra Seminar\n\n\nAbstract\nEtale af
fine representations of Lie algebras and algebraic groups arise in the con
text\nof affine geometry on Lie groups\, operad theory\, deformation theor
y and Young-Baxter equations.\nFor reductive groups\, every etale affine r
epresentation is equivalent to a\nlinear representation and we obtain a sp
ecial case of a prehomogeneous representation.\nSuch representations have
been classified by Sato and Kimura in some cases. The induced\nrepresentat
ion on the Lie algebra level gives rise to a pre-Lie algebra structure on
the\nLie algebra g of G. For a Lie group G\, a pre-Lie algebra structure o
n g corresponds to a\nleft-invariant affine structure on G. This refers to
a well-known question by John Milnor from 1977\non the existence of compl
ete left-invariant affine structures on solvable Lie groups.\n\nWe present
results on the existence of etale affine representations of reductive gro
ups and Lie algebras\nand discuss a related conjecture of V. Popov concern
ing flattenable groups and linearizable\nsubgroups of the affine Cremona g
roup.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willem Adriaan De Graaf (University of Trento\, Italy)
DTSTART:20230306T150000Z
DTEND:20230306T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/9
DESCRIPTION:Title: Computing the first Galois cohomology set of a reductive algebraic gr
oup\nby Willem Adriaan De Graaf (University of Trento\, Italy) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn classificat
ion problems over the real field R first Galois cohomology sets play an im
portant role\, as they often make it possible to classify the orbits of a
real Lie group. In this talk\, we outline an algorithm to compute the firs
t Galois cohomology set $H^1(G\,R)$ of a complex reductive algebraic group
G defined over the real field R. The algorithm is in a large part based o
n computations in the Lie algebra of G. This is joint work with Mikhail Bo
rovoi.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adela Latorre (Polytechnic University of Madrid\, Spain)
DTSTART:20230313T150000Z
DTEND:20230313T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/10
DESCRIPTION:Title: Solvable Lie algebras with complex symplectic structures\nby Ade
la Latorre (Polytechnic University of Madrid\, Spain) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nLet $\\mathfrak g$ be a $2n
$-dimensional solvable Lie algebra. A complex structure on $\\mathfrak g$
is an endomorphism $J$ that satisfies $J^2=-Id$ and $N_J(X\,Y)=0$\, for ev
ery $X\,Y\\in\\mathfrak g$\, being\n$$N_J(X\,Y):=[X\,Y]+J[JX\,Y]+J[X\,JY]-
[JX\,JY].$$ \nSuppose that $\\mathfrak g$ simultaneously admits a complex
structure $J$ and a symplectic structure $\\omega$ (i.e.\, a closed $2$-fo
rm $\\omega\\in\\wedge^2\\mathfrak g^*$ such that $\\omega^n\\neq 0$). \nA
lthough $J$ and $\\omega$ are initially two unrelated structures\, one can
ask for an additional condition involving both of them.\nIn this sense\,
the pair $(J\,\\omega)$ is said to be a complex symplectic structure if $J
$ is symmetric with respect to $\\omega$\, in the sense that $\\omega(JX\,
Y)=\\omega(X\,JY)$\, for every $X\,Y\\in\\mathfrak g$.\nIn this talk\, we
will present some methods to find certain types of solvable Lie algebras (
such as nilpotent or almost Abelian) admitting complex symplectic structur
es.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (University at Albany\, USA)
DTSTART:20230320T150000Z
DTEND:20230320T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/11
DESCRIPTION:Title: A generalization of the Murnaghan-Nakayama rule for K-k-Schur and k-
Schur functions\nby Duc-Khanh Nguyen (University at Albany\, USA) as p
art of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe introduc
e a generalization of K-k-Schur functions and k-Schur functions via the Pi
eri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized f
unctions. The rule are described explicitly in the cases of K-k-Schur func
tions and k-Schur functions\, with concrete descriptions and algorithms fo
r coefficients. Our work recovers the result of Bandlow\, Schilling\, and
Zabrocki for k-Schur functions\, and explains it as a degeneration of the
rule for K-k-Schur functions. In particular\, many other special cases pro
mise to be detailed in the future.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Usefi (Memorial University of Newfoundland\, Canada)
DTSTART:20230327T150000Z
DTEND:20230327T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/12
DESCRIPTION:Title: Polynomial identities\, group rings and enveloping algebras\nby
Hamid Usefi (Memorial University of Newfoundland\, Canada) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nI will talk about the
development of the theory of polynomial identities initiated by important
questions such as Burnside's asking if every finitely generated torsion
group is finite. The field was enriched by contributions of many great ma
thematicians. Most notably Lie rings methods were developed and used by Ze
lmanov in the 1990s to give a positive solution to the restricted Burnsid
e problem which awarded him the Fields medal. It has been of great interes
t to expand the theory to other varieties of algebraic structures. In part
icular\, I will review when a group algebra or enveloping algebra satisfy
a polynomial identity.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fairon (University of Paris-Saclay\, France)
DTSTART:20230410T150000Z
DTEND:20230410T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/13
DESCRIPTION:Title: Around Van den Bergh's double brackets\nby Maxime Fairon (Univer
sity of Paris-Saclay\, France) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nThe notion of a double Poisson bracket on an assoc
iative algebra was introduced by M. Van den Bergh in order to induce a (us
ual) Poisson bracket on the representation spaces of this algebra. I will
start by reviewing the basics of this theory and its relation to other int
eresting operations\, such as Leibniz brackets and $H_0$-Poisson structure
s. I will then explain some recent results and generalisations related to
double Poisson brackets.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaiming Zhao (Wilfrid Laurier University\, Waterloo\, Canada)
DTSTART:20230529T150000Z
DTEND:20230529T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/14
DESCRIPTION:Title: Simple smooth modules\nby Kaiming Zhao (Wilfrid Laurier Universi
ty\, Waterloo\, Canada) as part of European Non-Associative Algebra Semina
r\n\n\nAbstract\nLet L be a graded Lie algebra by integers with k-th homog
enous space $L_k$ where k are integers. An L-module V is called a smooth m
odule if any vector in V can be annihilated by $L_k$ for all sufficiently
large k. Smooth modules for affine Kac-Moody algebras were introduced and
studied by Kazhdan and Lusztig in 1993. I will show why this class of modu
les should be studied and what results are known now. An easy characteriza
tion for simple smooth modules for some Lie algebras will be provided.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marzia Mazzotta (University of Salento\, Italy)
DTSTART:20230417T150000Z
DTEND:20230417T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/15
DESCRIPTION:Title: Classification of set-theoretical solutions to the pentagon equation
\nby Marzia Mazzotta (University of Salento\, Italy) as part of Europe
an Non-Associative Algebra Seminar\n\n\nAbstract\nThe pentagon equation cl
assically originates from the field of Mathematical Physics. Our attention
is placed on the study of set-theoretical solutions of this equation\, na
mely\, maps $s: X \\times X \\to X \\times X$ given by $s(x\, y)=(xy\, \\t
heta_x(y))$\, where $X$ is a semigroup and $\\theta_x:X \\to X$ is a map s
atisfying two laws. In this talk\, we give some recent descriptions of so
me classes of solutions achieved starting from particular semigroups. Into
the specific\, we provide a characterization of \\emph{idempotent-invaria
nt} solutions on a Clifford semigroup $X$\, that are those for which $\\th
eta_a$ remains invariant on the set of idempotents $E(X)$. In addition\, w
e will focus on the classes of \\emph{involutive} and \\emph{idempotent} s
olutions\, which are solutions fulfilling $s^2=id_{X \\times X}$ and $s^2=
s$\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Přemysl Jedlička (Czech University of Life Sciences\, Czechia)
DTSTART:20230403T150000Z
DTEND:20230403T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/16
DESCRIPTION:Title: Non-degenerate involutive set-theoretic solutions of the Yang-Baxter
equation of multipermutation level 2\nby Přemysl Jedlička (Czech Un
iversity of Life Sciences\, Czechia) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nSet-theoretic solution of the Yang-Baxter eq
uation is a mapping $r:X\\times X\\to X\\times X$ satisfying\n\\[ (r\\time
s 1) (1\\times r) (r\\times 1) = (1\\times r) (r\\times 1) (1\\times r). \
\]\nA solution $r: (x\,y)\\mapsto (\\sigma_x(y)\,\\tau_y(x))$ is called no
n-degenerate if the mappings $\\sigma_x$ and $\\tau_y$ are permutations\,
for all $x\,y\\in X$. A solution is called involutive if $r^2=1$.\n\nIf $(
X\,r)$ is a non-degenerate involutive solution $(X\,r)$ then the relation~
$\\sim$ defined by $x\\sim y\\equiv \\sigma_x=\\sigma_y$ is a congruence.
A solution is of multipermutation level 2 if $|(X/\\sim)/\\sim|=1$.\n\nIn
our talk we focus on these solutions and we present several constructions
and properties.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malihe Yousofzadeh (University of Isfahan\, Iran)
DTSTART:20230522T150000Z
DTEND:20230522T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/17
DESCRIPTION:Title: Finite Weight Modules over Affine Lie Superalgebras\nby Malihe Y
ousofzadeh (University of Isfahan\, Iran) as part of European Non-Associat
ive Algebra Seminar\n\n\nAbstract\nNonzero real vectors of an affine Lie s
uperalgebra act on a simple module either locally nilpotently or injective
ly. This helps us to divide simple finite weight modules over a twisted af
fine Lie superalgebra $\\mathfrak{L}$ into two subclasses called hybrid an
d tight. We will talk about the characterization as well as the classifica
tion problem of modules in each subclass. In this regard\, the classificat
ion of bases of the root system of $\\mathfrak{L}$ is crucial. We will dis
cuss how we can classify the bases and how we can use the obtained classif
ication to study simple finite weight modules over $\\mathfrak{L}.$\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhe Sheng (Jilin University\, China)
DTSTART:20230508T090000Z
DTEND:20230508T100000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/18
DESCRIPTION:Title: Rota-Baxter operators and post-groups\nby Yunhe Sheng (Jilin Uni
versity\, China) as part of European Non-Associative Algebra Seminar\n\n\n
Abstract\nRota-Baxter operators on Lie algebras were first studied by Bela
vin\, Drinfeld and Semenov-Tian-Shansky as operator forms of the classical
Yang-Baxter equation. Integrating the Rota-Baxter operators on Lie algebr
as\, we introduce the notion of Rota-Baxter operators on Lie groups and mo
re generally on groups. Then the factorization theorem can be achieved dir
ectly on groups. We introduce the notion of post-Lie groups\, whose differ
entiations are post-Lie algebras. A Rota-Baxter operator on a group natura
lly induces a post-group. Post-groups are also closely related to operads\
, braces\, Lie-Butcher groups and various structures.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mátyás Domokos (Alfréd Rényi Institute of Mathematics\, Hungar
y)
DTSTART:20230508T150000Z
DTEND:20230508T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/19
DESCRIPTION:Title: An application of classical invariant theory to the study of identit
ies and concomitants of irreducible representations of the simple 3-dimens
ional complex Lie algebra\nby Mátyás Domokos (Alfréd Rényi Institu
te of Mathematics\, Hungary) as part of European Non-Associative Algebra S
eminar\n\n\nAbstract\nTo an $n$-dimensional representation of a finite dim
ensional Lie algebra one can naturally associate an algebra of equivariant
polynomial maps from the space of $m$-tuples of elements of the Lie algeb
ra into the space of $n$-by-$n$ matrices. In the talk we mainly deal with
the special case of irreducible\nrepresentations of the simple $3$-dimensi
onal complex Lie algebra\, and discuss results on the generators of the co
rresponding associative algebra of concomitants as well as results on the
quantitative behaviour of the identities of these representations.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rutwig Campoamor Stursberg (Complutense University of Madrid\, Spa
in)
DTSTART:20230605T150000Z
DTEND:20230605T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/20
DESCRIPTION:Title: Commutants of subalgebras in universal enveloping algebras\nby R
utwig Campoamor Stursberg (Complutense University of Madrid\, Spain) as pa
rt of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe problem
of determining centralizers in the enveloping algebras of Lie algebras is
considered from both the algebraic and analytical perspectives. Applicatio
ns of the procedure\, such as the decomposition problem of the enveloping
algebra of a simple Lie algebra\, the labelling problem and the constructi
on of orthonormal bases of states are considered.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis Topley (University of Bath\, UK)
DTSTART:20230515T090000Z
DTEND:20230515T100000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/21
DESCRIPTION:Title: Modular representation theory and finite W-algebras\nby Lewis To
pley (University of Bath\, UK) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nFinite W-algebras were introduced by Premet in ful
l generality\, and they quickly became quite famous for their many applica
tions in the representation theory of complex semisimple Lie algebras\, es
pecially the classification of primitive ideals. However\, these algebras
first appeared in the representation theory of Lie algebras associated to
reductive groups in positive characteristic. In this talk I will survey th
e history of finite W-algebras in modular representation theory\, and expl
ain some of the contributions I have made to the field. The main applicati
ons in this talk will be the construction and classification of``small'
' modules of Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Castilho de Mello (Federal University of São Paulo\, Brazi
l)
DTSTART:20230424T150000Z
DTEND:20230424T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/22
DESCRIPTION:Title: Images of polynomials on algebras\nby Thiago Castilho de Mello (
Federal University of São Paulo\, Brazil) as part of European Non-Associa
tive Algebra Seminar\n\n\nAbstract\nThe so-called Lvov-Kaplansky Conjectur
e states that the image of a multilinear polynomial evaluated on the matri
x algebra or order n is always a vector subspace. A solution to this probl
em is known only for $n=2$. In this talk we will present analogous conject
ures for other associative and non-associative algebras and for graded alg
ebras. Also\, we will show how we can use gradings to present a statement
equivalent to the Lvov-Kaplansky conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Mattarei (University of Lincoln\, UK)
DTSTART:20230612T150000Z
DTEND:20230612T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/23
DESCRIPTION:Title: Graded Lie algebras of maximal class\nby Sandro Mattarei (Univer
sity of Lincoln\, UK) as part of European Non-Associative Algebra Seminar\
n\n\nAbstract\nThe title matches that of a series of papers by various aut
hors beginning in 1997\, whose goal was the study and classification of su
ch algebras over fields of positive characteristic. The original motivatio
n came from group theory: the Leedham-Green and Newman coclass conjectures
on pro-p groups from 1980 had all become theorems relatively recently\, a
nd subsequent results of Shalev and Zelmanov had raised interest in what o
ne could say about Lie algebras of finite coclass. In positive characteris
tic\, the simplest case of coclass one (i.e.\, 'Lie algebras of maximal cl
ass'\, also called 'filiform' in some quarters) appeared challenging even
under the strong assumptions of those Lie algebras being infinite-dimensio
nal and graded over the positive integers. I will review motivations and r
esults of those studies\, including some classifications obtained by Caran
ti\, Newman\, Vaughan-Lee. Then I will describe some generalizations recen
tly established with three of my former PhD students.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther García González (King Juan Carlos University\, Spain)
DTSTART:20230626T150000Z
DTEND:20230626T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/24
DESCRIPTION:Title: Nilpotent last-regular elements\nby Esther García González (Ki
ng Juan Carlos University\, Spain) as part of European Non-Associative Alg
ebra Seminar\n\n\nAbstract\nWe say that an element $x$ in a ring $R$ is ni
lpotent last-regular if it is nilpotent of certain index $n+1$ and its las
t nonzero power $x^n$ is regular von Neumann\, i.e.\, there exists another
element $y\\in R$ such that $x^nyx^n=x^n$. This type of elements naturall
y arise when studying certain inner derivations in the Lie algebra $\\Skew
(R\,*)$ of a ring $R$ with involution $*$ whose indices of nilpotence diff
er when considering them acting as derivations on $\\Skew(R\,*)$ and on th
e whole $R$. When moving to the symmetric Martindale ring of quotients $Q^
s_m(R)$ of $R$ we still obtain inner derivations with the same indices of
nilpotence on $Q^s_m(R)$ and on the skew-symmetric elements $\\Skew(Q^s_m(
R)\,*)$ of $Q^s_m(R)$\, but with the extra condition of being generated by
a nilpotent last-regular element. This condition strongly determines the
structure of $Q^s_m(R)$ and of $\\Skew(Q^s_m(R)\,*)$. \nWe will review the
Jordan canonical form of nilpotent last-regular elements and show how to
get gradings in associative algebras (with and without involution) when th
ey have such elements.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigiswald Barbier (Ghent University\, Belgium)
DTSTART:20230703T150000Z
DTEND:20230703T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/25
DESCRIPTION:Title: Diagram categories of Brauer type\nby Sigiswald Barbier (Ghent U
niversity\, Belgium) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nDiagram categories are a special kind of tensor categories t
hat can be represented using diagrams. In this talk I will give an introdu
ction to categories represented using Brauer diagrams. In particular I wil
l explain the relation with the Brauer algebra and how the categorical fra
mework can be applied to representation theory of the corresponding algebr
a.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Arzhantsev (HSE University\, Russia)
DTSTART:20230515T150000Z
DTEND:20230515T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/26
DESCRIPTION:Title: Uniqueness of addition in Lie algebras\nby Ivan Arzhantsev (HSE
University\, Russia) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nWe say that a Lie ring R is called a unique addition Lie rin
g\, or briefly a UA-Lie ring\, if any commutator-preserving bijection on R
preserves the addition as well. We prove that any semisimple Lie algebra
and any its parabolic subalgebra is a UA-Lie ring. Also we describe wide c
lasses of solvable UA-Lie rings.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (University of Strasbourg\, France)
DTSTART:20230424T090000Z
DTEND:20230424T100000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/27
DESCRIPTION:Title: Operad filtrations and quantization\nby Vladimir Dotsenko (Unive
rsity of Strasbourg\, France) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nThe celebrated problem of deformation quantization
discusses deformations of Poisson algebras into associative algebras\, a q
uestion that is\, in the end\, motivated by quantum mechanics. I shall dis
cuss this question and some of its generalisations from the purely algebra
ic point of view using the theory of operads. In particular\, I shall show
how to prove that there are\, in a strict mathematical sense\, only two m
eaningful deformation problems for Poisson algebras\, namely deforming the
m in the class of all Poisson algebras or all associative algebras\, and t
here is only one meaningful deformation problem for the so called almost P
oisson algebras (also sometimes known as generic Poisson algebras)\, namel
y deforming them in the class of all almost Poisson algebras. For instance
\, this explains the existing body of work in the mathematical physics lit
erature asserting that some classes of non-associative star products canno
t be alternative\, are always flexible etc.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Csaba Schneider (Federal University of Minas Gerais\, Brazil)
DTSTART:20230821T150000Z
DTEND:20230821T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/28
DESCRIPTION:Title: Computing invariants of some nilpotent Lie algebras\nby Csaba Sc
hneider (Federal University of Minas Gerais\, Brazil) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nI will present some interes
ting computations concerning polynomial and rational invariants of nilpote
nt Lie algebras. I will say more about standard filiform Lie algebras whic
h appear to have the highest level of complication among the small-dimensi
onal algebras. I will outline an implementable algorithm for the computati
on of generators of the field of rational invariants.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Facchini (University of Padua\, Italy)
DTSTART:20230814T150000Z
DTEND:20230814T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/29
DESCRIPTION:Title: Heaps and trusses\nby Alberto Facchini (University of Padua\, It
aly) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nI
will present the first notions concerning heaps and trusses. Heaps were in
troduced for the first time by H. Prüfer (1924) and R. Baer (1929). A he
ap is a pair $(H\, [−\,−\,−])$ consisting of a set $H$ and a ternary
operation $$[−\,−\,−] : H \\times H \\times H \\to H\, (x\, y\, z)
\\to [x\, y\, z]\,$$ such that\, for all $v\, w\, x\, y\, z \\in H\,$
\n$$[v\, w\, [x\, y\, z]] = [[v\, w\, x\, ]\, y\, z]\, \\ [x\, x\, y] = y\
,\\ [y\, x\, x]= y.$$\n Truss is a much more recent algebraic structure (T
. Brzeziński\, 2019). A truss is a heap with a further associative binar
y operation\, denoted by juxtaposition\, which distributes over $[−\,−
\,−]\,$ that is\, for all $w\, x\, y\, z \\in T\,$ \n$$w[x\, y\, z] = [w
x\, wy\, wz]\, \\ [x\, y\, z]w = [xw\, yw\, zw]\,\\ [x\, y\, z] =[z\, y\,
x].$$\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elitza Hristova (Institute of Mathematics and Informatics\, Bulgar
ia)
DTSTART:20230828T150000Z
DTEND:20230828T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/30
DESCRIPTION:Title: On the GL(n)-module structure of Lie nilpotent associative relativel
y free algebras\nby Elitza Hristova (Institute of Mathematics and Info
rmatics\, Bulgaria) as part of European Non-Associative Algebra Seminar\n\
n\nAbstract\nLet $K\\langle X\\rangle$ denote the free associative algebra
generated by a finite set $X$ with n elements over a field $K$ of charact
eristic 0. Let $I_p$ denote the two-sided associative ideal in $K\\langle
X\\rangle$ generated by all commutators of length $p$\, where $p$ is an ar
bitrary positive integer greater than 1. The group ${\\rm GL(n)}$ acts in
a natural way on the quotient $K\\langle X\\rangle/I_p$ and the ${\\rm GL(
n)}$-module structure of $K\\langle X\\rangle/I_p$ is known for $p=2\,3\,4
\,5$. In this talk\, we give some results on the ${\\rm GL}(n)$-module str
ucture of $K\\langle X\\rangle/I_p$ for any $p$. More precisely\, we give
a bound on the values of the highest weights of irreducible ${\\rm GL}(n)$
-modules which appear in the decomposition of $K\\langle X\\rangle/I_p$. W
e discuss also applications of these results related to the algebras of G-
invariants in $K\\langle X\\rangle/I_p$\, where G is one of the classical
${\\rm GL}(n)$-subgroups ${\\rm SL}(n)$\, ${\\rm O}(n)$\, ${\\rm SO}(n)$\,
or ${\\rm Sp}(2k)$ (for $n=2k$).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Macedo (Federal University of São Paulo\, Brazil)
DTSTART:20230710T150000Z
DTEND:20230710T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/31
DESCRIPTION:Title: Finite-dimensional modules for map superalgebras\nby Tiago Maced
o (Federal University of São Paulo\, Brazil) as part of European Non-Asso
ciative Algebra Seminar\n\n\nAbstract\nIn this talk we will present recent
results on the category of finite-dimensional modules for map superalgebr
as. Firstly\, we will show a new description of certain irreducible module
s. Secondly\, we will use this new description to extract homological prop
erties of the category of finite-dimensional modules for map superalgebras
\, most importantly\, its block decomposition.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires\, Argentina)
DTSTART:20230724T150000Z
DTEND:20230724T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/32
DESCRIPTION:Title: Tamarkin-Tsygan calculus for gentle algebras\nby Andrea Solotar
(University of Buenos Aires\, Argentina) as part of European Non-Associati
ve Algebra Seminar\n\n\nAbstract\nThe whole structure given by the Hochsch
ild cohomology and homology of an associative algebra A together with the
cup and cap products\, the Gerstenhaber bracket and the Connes differentia
l is called the Tamarkin-Tsygan calculus. It is invariant under derived eq
uivalence and if we can compute all these invariants provides a lot of inf
ormation. The calculation of the whole Tamarkin-Tsygan calculus is very di
fficult and generally not even possible for particular algebras. However\,
there exist some calculations for individual algebras. The problem is\, i
n general\, that the minimal projective bimodule resolutions are difficult
to find and even if one is able to compute such a resolution\, it might b
e so complicated that the computation of the Tamarkin-Tsygan calculus is n
ot within reach. For monomial algebras the minimal projective bimodule res
olution is known and in the case of quadratic monomial algebras it is simp
le enough\, to embark on the extensive calculations of the Tamarkin Tsygan
calculus. Yet even for quadratic monomial algebras\, the combinatorial le
vel of the calculations is such\nthat it is too complicated to calculate t
he whole calculus. On the other hand for gentle algebras\, the additional
constraints on their structure are such that the calculations become possi
ble. We will focus on the concrete aspects of these calculations.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Petukhov (Institute for Information Transmission Problems\,
Russia)
DTSTART:20230717T150000Z
DTEND:20230717T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/33
DESCRIPTION:Title: Witt Lie algebra and the associated primitive ideals\nby Alexey
Petukhov (Institute for Information Transmission Problems\, Russia) as par
t of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn my talk I
would like to discuss my joint articles with S. Sierra about the primitive
ideals of universal enveloping U(W) and the symmetric algebra S(W) of Wit
t Lie algebra W and similar Lie algebras (including Virasoro Lie algebra).
The key theorem in this setting is that every nontrivial quotient by a tw
o-sided ideal of U(W) or S(W) has finite Gelfand-Kirillov dimension. Toget
her with S. Sierra we enhanced this statement to the description of primit
ive Poisson ideals of S(W) in terms of certain points on the complex plane
plus a few parameters attached to these points. In the end I will try to
explain how all these concepts works for the ideals whose quotient has Gel
fand-Kirillov dimension 2.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Şehmus Fındık (Çukurova University\, Turkey)
DTSTART:20230731T150000Z
DTEND:20230731T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/34
DESCRIPTION:Title: Symmetric polynomials in some certain noncommutative algebras\nb
y Şehmus Fındık (Çukurova University\, Turkey) as part of European Non
-Associative Algebra Seminar\n\n\nAbstract\nLet F be a finitely generated
free algebra in a variety of algebras over a field of characteristic zero.
A polynomial in F is called symmetric if it is preserved under any permut
ation of the generators. The set S(F) of symmetric polynomials is a subalg
ebra of F. In this talk\, we examine the algebras S(F)\, where F is the fr
ee metabelian associative\, Lie\, Leibniz\, Poisson algebra or the free al
gebra generated by generic traceless matrices or the free algebra in the v
ariety generated by Grassmann algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lleonard Rubio y Degrassi (Uppsala University\, Sweden)
DTSTART:20230807T150000Z
DTEND:20230807T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/35
DESCRIPTION:Title: Hochschild cohomology groups under gluing idempotents\nby Lleona
rd Rubio y Degrassi (Uppsala University\, Sweden) as part of European Non-
Associative Algebra Seminar\n\n\nAbstract\nStable equivalences occur frequ
ently in the representation theory of finite-dimensional algebras\; howeve
r\, these equivalences are poorly understood. An interesting class of stab
le equivalences is obtained by ‘gluing’ two idempotents. More precisel
y\, let A be a finite-dimensional algebra with a simple projective module
and a simple injective module. Assume that B is a subalgebra of A having t
he same Jacobson radical. Then B is constructed by identifying the two ide
mpotents belonging to the simple projective module and to the simple injec
tive module\, respectively. \n\nIn this talk\, we will compare the first H
ochschild cohomology groups of finite-dimensional monomial algebras under
gluing two arbitrary idempotents (hence not necessarily inducing a stable
equivalence). As a corollary\, we will show that stable equivalences obtai
ned by gluing two idempotents provide 'some functoriality' to the first Ho
chschild cohomology\, that is\, HH^1(A) is isomorphic to a quotient of HH^
1(B).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykola Khrypchenko (Univesity of Porto\, Portugal)
DTSTART:20230904T150000Z
DTEND:20230904T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/36
DESCRIPTION:Title: Transposed Poisson structures\nby Mykola Khrypchenko (Univesity
of Porto\, Portugal) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nA transposed Poisson algebra is a triple (L\,⋅\,[⋅\,⋅]
) consisting of a vector space L with two bilinear operations ⋅ and [⋅
\,⋅]\, such that (L\,⋅) is a commutative associative algebra\; (L\,[
⋅\,⋅]) is a Lie algebra\; the "transposed" Leibniz law holds: 2z⋅[x\
,y]=[z⋅x\,y]+[x\,z⋅y] for all x\,y\,z∈L. A transposed Poisson algebr
a structure on a Lie algebra (L\,[⋅\,⋅]) is a (commutative associative
) multiplication ⋅ on L such that (L\,⋅\,[⋅\,⋅]) is a transposed P
oisson algebra. I will give an overview of my recent results in collaborat
ion with Ivan Kaygorodov (Universidade da Beira Interior) on classificatio
n of transposed Poisson structures on several classes of Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bauyrzhan Sartayev (Suleyman Demirel University\, Kazakhstan)
DTSTART:20230911T150000Z
DTEND:20230911T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/37
DESCRIPTION:Title: Binary perm algebras and alternative algebras\nby Bauyrzhan Sart
ayev (Suleyman Demirel University\, Kazakhstan) as part of European Non-As
sociative Algebra Seminar\n\n\nAbstract\nWe describe the defining identiti
es of a variety of binary perm algebras which is a subvariety of the varie
ty of alternative algebras. Moreover\, we construct a basis of the free bi
nary perm algebra. In addition\, we describe the subalgebras of binary per
m algebras under commutator which has a connection with Malcev algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hader Elgendy (Damietta University\, Egypt)
DTSTART:20230925T150000Z
DTEND:20230925T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/38
DESCRIPTION:Title: On Jordan quadruple systems\nby Hader Elgendy (Damietta Universi
ty\, Egypt) as part of European Non-Associative Algebra Seminar\n\n\nAbstr
act\nWe present the recent results on Jordan quadruple systems. We show th
e Peirce decomposition for a Jordan quadruple system with respect to a qua
dripotent. We extend the notions of the orthogonality\, primitivity\, and
minimality of tripotents in a Jordan triple system to that of quadripotent
s\nin a Jordan quadruple system. We show the relation between minimal and
primitive quadripotents in a Jordan quadruple system. We also discuss the
results on complemented subsystems of Jordan quadruple systems.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfilgen Sebandal (Mindanao State University\, Philippines)
DTSTART:20231002T150000Z
DTEND:20231002T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/39
DESCRIPTION:Title: Finite graded classification conjecture for Leavitt path algebras\nby Alfilgen Sebandal (Mindanao State University\, Philippines) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nGiven a directe
d graph\, one can associate two algebraic entities: the Leavitt path algeb
ra and the talented monoid. The Graded Classification conjecture states th
at the talented monoid could be a graded invariant for the Leavitt path al
gebra\, i.e.\, isomorphism in the talented monoids reflects as graded equi
valence in the category of graded modules over the Leavitt path algebra of
the corresponding directed graphs. In this talk\, we shall see confirmati
ons of this invariance in the ideal structure of the talented monoid with
the so-called Gelfand-Kirillov Dimension of the Leavitt path algebra. The
last part of the talk is an affirmation of the Graded classification conje
cture in the finite-dimensional case. This is a compilation of joint works
with Roozbeh Hazrat\, Wolfgang Bock\, and Jocelyn P. Vilela.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Chapman (Academic College of Tel-Aviv-Yaffo\, Israel)
DTSTART:20230918T150000Z
DTEND:20230918T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/40
DESCRIPTION:Title: Roots and Critical Points of Cayley-Dickson Algebras\nby Adam Ch
apman (Academic College of Tel-Aviv-Yaffo\, Israel) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\n"We study the roots and criti
cal points (i.e.\, points at which the formal derivative vanishes) of stan
dard polynomials over Cayley-Dickson algebras.\nIn the anisotropic real ca
se\, we prove that the critical points live inside the convex hull of the
roots of the polynomial.\nThe talk is based on joint work with Alexander G
uterman\, Solomon Vishkautsan and Svetlana Zhilina."\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Vojtěchovský (University of Denver\, USA)
DTSTART:20231030T150000Z
DTEND:20231030T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/41
DESCRIPTION:Title: Solvability and nilpotence just beyond groups\nby Petr Vojtěcho
vský (University of Denver\, USA) as part of European Non-Associative Alg
ebra Seminar\n\n\nAbstract\nSolvability and nilpotence arise naturally fro
m the commutator theory in congruence modular varieties. In the presence o
f associativity\, the resulting concepts agree with the classical concepts
of group theory. But the two kinds of solvability differ in loops ( = not
necessarily associative groups) and it is a difficult question to determi
ne the boundary where the two theories coincide. I will review the general
theory and report on recent results\, particularly in Moufang loops. For
instance\, we will prove the Odd Order Theorem for Moufang loops for the s
tronger notion of solvability. This is joint work with Ales Drapal and Dav
id Stanovsky.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Gorbatsevich (Russian State Technological University name
d after K.E. Tsiolkovky\, Russia)
DTSTART:20231009T150000Z
DTEND:20231009T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/42
DESCRIPTION:Title: On some classes of bases in finite-dimensional Lie algebras\nby
Vladimir Gorbatsevich (Russian State Technological University named after
K.E. Tsiolkovky\, Russia) as part of European Non-Associative Algebra Semi
nar\n\n\nAbstract\nLie algebras having bases of a special form (nice and b
eautiful bases) are considered. For nice bases\, it is proved that in any
nilpotent Lie algebra their number (up to equivalence) is finite. For som
e Lie algebras of low dimension\, it is shown that\, when passing from a c
omplex Lie algebra to its realification\, the property to have a beautifu
l basis is lost. Also nilpotent Lie algebras of dimensions less than 8 are
considered.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Markl (The Czech Academy of Sciences\, Czechia)
DTSTART:20231023T150000Z
DTEND:20231023T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/43
DESCRIPTION:Title: Transfers of strongly homotopy structures as Grothendieck bifibratio
ns\nby Martin Markl (The Czech Academy of Sciences\, Czechia) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nIt is well-know
n that strongly homotopy structures can be transferred over chain homotopy
equivalences. Using the uniqueness results of Markl & Rogers we show that
the transfers could be organized into a discrete Grothendieck bifibration
. An immediate aplication is e.g. functoriality up to isotopy.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guodong Zhou (East China Normal University\, China)
DTSTART:20231016T150000Z
DTEND:20231016T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/44
DESCRIPTION:Title: The homotopy theory of operated algebras\nby Guodong Zhou (East
China Normal University\, China) as part of European Non-Associative Algeb
ra Seminar\n\n\nAbstract\nThe talk is a survey of our recent results on th
e homotopy theory of operated algebras such as Rota-Baxter associative (or
Lie) algebras and differential associative (or Lie) algebras etc. We make
explicit the Kozul dual homotopy cooperads and the minimal models of the
operads governing these operated algebras. As a consequence the L-infinity
structures on the deformation complexes are described as well.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:František Marko (Pennsylvania State University\, USA)
DTSTART:20231113T150000Z
DTEND:20231113T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/45
DESCRIPTION:Title: Blocks of rational supermodules over some quasi-reductive supergroup
s in positive characteristic\nby František Marko (Pennsylvania State
University\, USA) as part of European Non-Associative Algebra Seminar\n\n\
nAbstract\nThis is an overview of joint work with Alexandr N. Zubkov. We d
iscuss linkage principles and blocks for general linear\, ortho-symplectic
\, and periplectic supergroups over fields of positive characteristics. In
the end\, we describe the strong linkage principle and blocks for the que
er supergroup Q(2)."\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Senne Trappeniers (Free University of Brussels\, Belgium)
DTSTART:20231127T150000Z
DTEND:20231127T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/46
DESCRIPTION:Title: The interplay between skew braces\, the Yang–Baxter equation and H
opf–Galois structures\nby Senne Trappeniers (Free University of Brus
sels\, Belgium) as part of European Non-Associative Algebra Seminar\n\n\nA
bstract\nIn 2007\, Wolfgang Rump introduced algebraic objects called brace
s\, these gen- eralise Jacobson radical rings and are related to involutiv
e non-degenerate set- theoretic solutions of the Yang–Baxter equation (Y
BE). These objects were subse- quently generalised to skew braces by Leand
ro Guarnieri and Leandro Vendramin in 2017\, and a similar relation was sh
own to hold for non-degenerate set-theoretic solutions of the YBE which ar
e not necessarily involutive. In this talk\, we will de- scribe this inter
play between skew braces and the YBE. We will also discuss their relation
to Hopf–Galois structures and see how this extends the classical Galois
theory in an elegant way.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Zhilina (Lomonosov Moscow State University\, Russia)
DTSTART:20231106T150000Z
DTEND:20231106T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/47
DESCRIPTION:Title: On the lengths of Okubo algebras\nby Svetlana Zhilina (Lomonosov
Moscow State University\, Russia) as part of European Non-Associative Alg
ebra Seminar\n\n\nAbstract\nThe length function of a non-associative algeb
ra describes the guaranteed number of multiplications which will be suffic
ient to generate the whole algebra with its arbitrary generating set. In t
his talk we present a new method for length computation based on the seque
nce of differences between the dimensions of a certain sequence of subspac
es. It allows us to compute the length of an Okubo algebra A over an arbit
rary field. Namely\, if A contains either nonzero idempotents or zero divi
sors\, then its length equals four\, and otherwise its length equals three
. We also show that\, in the latter case\, A is generated by any two eleme
nts which do not belong to the same two-dimensional subalgebra. The talk i
s based on a joint work with Alexander Guterman.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Lopatin (University of Campinas\, Brazil)
DTSTART:20231120T150000Z
DTEND:20231120T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/48
DESCRIPTION:Title: Polynomial invariants for two dimensional algebras\nby Artem Lop
atin (University of Campinas\, Brazil) as part of European Non-Associative
Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Fernández Ouaridi (University of Coimbra\, Portugal)
DTSTART:20231204T150000Z
DTEND:20231204T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/49
DESCRIPTION:Title: On the simple transposed Poisson algebras and Jordan superalgebras\nby Amir Fernández Ouaridi (University of Coimbra\, Portugal) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe prove that a
transposed Poisson algebra is simple if and only if its associated Lie br
acket is simple. Consequently\, any simple finite-dimensional transposed P
oisson algebra over an algebraically closed field of characteristic zero i
s trivial. Similar results are obtained for transposed Poisson superalgebr
as. An example of a non-trivial simple finite-dimensional transposed Poiss
on algebra is constructed by studying the transposed Poisson structures on
the modular Witt algebra. Furthermore\, we show that the Kantor double of
a transposed Poisson algebra is a Jordan superalgebra\, that is\, we prov
e that transposed Poisson algebras are Jordan brackets. Additionally\, a
simplicity criterion for the Kantor double of a transposed Poisson algebra
is obtained.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanne Pumpluen (University of Nottingham\, UK)
DTSTART:20231211T150000Z
DTEND:20231211T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/50
DESCRIPTION:Title: A way to generalize classical results from central simple algebras t
o the nonassociative setting\nby Susanne Pumpluen (University of Notti
ngham\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstr
act\nRecently\, the theory of semiassociative algebras and their Brauer mo
noid was introduced by Blachar\, Haile\, Matri\, Rein\, and Vishne as a
canonical generalization of the theory of associative central simple alge
bras and their Brauer group: together with the tensor product semiassociat
ive algebras over a field form a monoid that contains the classical Brauer
group as its unique maximal subgroup. We present classes of semiassociati
ve algebras that are canonical generalizations of classes of certain centr
al simple algebras and explore their behaviour in the Brauer monoid. Time
permitting\, we also discuss some - hopefully interesting - particularitie
s of this newly defined Brauer monoid.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio López-Permouth (Ohio University\, USA)
DTSTART:20240108T150000Z
DTEND:20240108T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/51
DESCRIPTION:Title: Basic Extension Modules (All bases are created equal\, but some are
more equal than others)\nby Sergio López-Permouth (Ohio University\,
USA) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe
report on ongoing research about a module-theoretic construction which\,
when successful\, yields natural extensions of infinite dimensional module
s over arbitrary algebras. Whether the construction works or not depends o
n the basis that one chooses to carry on such a construction. Bases that w
ork are said to be amenable. A natural example on which one may focus is w
hen the module is the algebra itself. For instance\, a great deal of the w
ork done so far has focused on infinite dimensional algebra of polynomials
on a single variable. We will see that amenability and related notions se
rve to classify the distinct bases according to interesting complementary
properties having to do with the types of relations induced on them by the
properties of their change-of-basis matrices.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Tkachev (Linköping University\, Sweden)
DTSTART:20240115T150000Z
DTEND:20240115T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/52
DESCRIPTION:Title: Some questions of nonassociative algebra from the idempotent point o
f view\nby Vladimir Tkachev (Linköping University\, Sweden) as part o
f European Non-Associative Algebra Seminar\n\n\nAbstract\nHow to recover a
n algebra structure if the algebra does NOT satisfy any reasonable identit
y? How to characterize its idempotents\, their spectrum\, or fusion laws?
In my talk\, I will discuss what can be thought of as "nonassociative alge
bra in large"\, imitating a well-known concept of "geometry in large". In
other words\, the properties of nonassociative algebras which crucially de
pend on a complete set of idempotents. The latter is very related to the c
oncept of generic algebras. I will explain some recent results in this dir
ection and some unsolved problems.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Friedrich Wagemann (University of Nantes\, France)
DTSTART:20240122T150000Z
DTEND:20240122T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/53
DESCRIPTION:Title: Cohomology of semi-direct product Lie algebras\nby Friedrich Wag
emann (University of Nantes\, France) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nThis is joint work with Dietrich Burde (Uni
versity of Vienna\, Austria). Intrigued by computations of Richardson\, ou
r goal is to compute the adjoint cohomology spaces of Lie algebras which a
re the semi-direct product of a simple Lie algebra s and an s-module. We p
resent some theorems and conjectures in these cohomologies.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyong Hong (Hangzhou Normal University\, China)
DTSTART:20240129T150000Z
DTEND:20240129T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/54
DESCRIPTION:Title: Novikov bialgebras\, infinite-dimensional Lie bialgebras and Lie con
formal bialgebras\nby Yanyong Hong (Hangzhou Normal University\, China
) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn th
is talk\, I will introduce a bialgebra theory for the Novikov algebra\, na
mely the Novikov bialgebra\, which is characterized by the fact that its a
ffinization (by a quadratic right Novikov algebra) gives an infinite-dimen
sional Lie bialgebra. A Novikov bialgebra is also characterized as a Manin
triple of Novikov algebras. The notion of Novikov Yang-Baxter equation is
introduced\, whose skewsymmetric solutions can be used to produce Novikov
bialgebras and hence Lie bialgebras. These solutions also give rise to sk
ewsymmetric solutions of the classical Yang-Baxter equation in the infinit
e-dimensional Lie algebras from the Novikov algebras. Moreover\, a similar
connection between Novikov bialgebras and Lie conformal bialgebras will b
e introduced. This talk is based on joint works with Chengming Bai and Li
Guo.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Buzaglo (University of Edinburgh\, UK)
DTSTART:20240205T150000Z
DTEND:20240205T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/55
DESCRIPTION:Title: Derivations\, extensions\, and rigidity of subalgebras of the Witt a
lgebra\nby Lucas Buzaglo (University of Edinburgh\, UK) as part of Eur
opean Non-Associative Algebra Seminar\n\n\nAbstract\nWe study Lie algebrai
c properties of subalgebras of the Witt algebra and the one-sided Witt alg
ebra: we compute derivations\, one-dimensional extensions\, and automorphi
sms of these subalgebras. In particular\, all these properties are inherit
ed from the full Witt algebra (e.g. derivations of subalgebras are simply
restrictions of derivations of the Witt algebra). We also prove that any i
somorphism between subalgebras of finite codimension extends to an automor
phism of the Witt algebra. We explain this "rigid" behavior by proving a u
niversal property satisfied by the Witt algebra as a completely non-split
extension of any of its subalgebras of finite codimension. This is a purel
y Lie algebraic property which I will introduce in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saïd Benayadi (University of Lorraine\, France)
DTSTART:20240212T150000Z
DTEND:20240212T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/56
DESCRIPTION:Title: On a class of pseudo-Euclidean left-symmetric algebras\nby Saïd
Benayadi (University of Lorraine\, France) as part of European Non-Associ
ative Algebra Seminar\n\n\nAbstract\nA pseudo-Euclidean left-symmetric alg
ebra $(A\, .\,< \, >)$ is a real left-symmetric algebra $(A\,.)$ endowed w
ith a non-degenerate symmetric bilinear form $< \, >$ such that left mult
iplications by any element of A are skew-symmetric with respect to $< \, >
$. We recall that a pseudo-Euclidean Lie algebra $(g\, [ \, ]\, < \, >)$ i
s flat if and only if $(g\, .\, \,< \, >)$ its underlying vector space en
dowed with the Levi-Civita product associated with $< \, >$ is a pseudo-Eu
clidean left-symmetric algebra. In this talk\, We will give an inductive c
lassification of pseudo-Euclidean left-symmetric algebras $(A\, .\,< \, >
)$ such that commutators of allelements of A are contained in the left ann
ihilator of $(A\, .)\,$ these algebras will be called pseudo-Euclidean lef
t-symmetric L−algebras of any signature. To do this\, we will develop do
uble extension processes that allow us to have inductive descriptions of a
ll pseudo-Euclidean left-symmetric $L$−algebras and of all its pseudo-Eu
clidean modules.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Hildebrandsson (Linköping University\, Sweden)
DTSTART:20240219T150000Z
DTEND:20240219T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/57
DESCRIPTION:Title: Octonion algebras over schemes and the equivalence of isotopes and i
sometric forms\nby Victor Hildebrandsson (Linköping University\, Swed
en) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn
2019\, Alsaody and Gille show that\, for octonion algebras over unital com
mutative rings\, there is an equivalence between isotopes and isometric qu
adratic forms. This leads us to a question: can this equivalence be genera
lized to octonion algebras over a (not necessarily affine) scheme? We give
the basic definitions of octonion algebras over schemes. We show that an
isotope of an octonion algebra C over a scheme is isomorphic to a twist by
an Aut(C)–torsor. We conclude by giving an affirmative answer to our qu
estion.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Gorshkov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20240226T150000Z
DTEND:20240226T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/58
DESCRIPTION:Title: Pseudo-composition algebras as axial algebras\nby Ilya Gorshkov
(Sobolev Institute of Mathematics\, Russia) as part of European Non-Associ
ative Algebra Seminar\n\n\nAbstract\nWe show that pseudo-composition algeb
ras and train algebras of rank 3 generated by idempotents are characterize
d as axial algebras with fusion laws derived from the Peirce decomposition
s of idempotents in these classes of algebras. The corresponding axial alg
ebras are called PC(η)-axial algebras\, where η is an element of the gro
und field. As a first step towards their classification\, we describe 2−
and 3-generated subalgebras of such algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Turner (University of Birmingham\, UK)
DTSTART:20240304T150000Z
DTEND:20240304T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/59
DESCRIPTION:Title: Skew Axial Algebras of Monster Type\nby Michael Turner (Universi
ty of Birmingham\, UK) as part of European Non-Associative Algebra Seminar
\n\n\nAbstract\nGiven a 2-generated primitive axial algebra of Monster Typ
e\, it has been shown that it has an axet which is regular or skew. With a
ll the known examples being regular\, it was proposed if any axial algebra
were skew and if so\, can they be classified. We will begin by defining a
xial algebras and axets\, before producing examples of axial algebras with
skew axets. We will finish by stating the complete classification of thes
e skew axial algebras and mention how it was proven.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Alejandra Alvarez (University of Antofagasta\, Chile)
DTSTART:20240311T150000Z
DTEND:20240311T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/60
DESCRIPTION:Title: On S-expansions and other transformations of Lie algebras\nby Ma
ría Alejandra Alvarez (University of Antofagasta\, Chile) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nThe aim of this work i
s to study the relation between S-expansions and other transformations of
Lie algebras. In particular\, we prove that contractions\, deformations an
d central extensions of Lie algebras are preserved by S-expansions. We als
o provide several examples and give conditions so transformations of reduc
ed subalgebras of S-expanded algebras are preserved by the S-expansion pro
cedure. This is a joint work with Javier Rosales-Gómez.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lopes (University of Porto\, Portugal)
DTSTART:20240325T150000Z
DTEND:20240325T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/62
DESCRIPTION:Title: Torsionfree representations of Smith algebras\nby Samuel Lopes (
University of Porto\, Portugal) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nWe will discuss representations of the Smith alge
bra which are free of finite rank over a subalgebra which plays a role ana
logous to that of the (enveloping algebra of the) Cartan subalgebra of the
simple Lie algebra $\\mathfrak{sl}_2$. In the case of rank 1 we obtain a
full description of the isomorphism classes\, a simplicity criterion\, and
a combinatorial algorithm to produce all composition series and the multi
plicities of the simple factors. This is joint work with V. Futorny (SUSTe
ch & USP) and E. Mendonça (Lyon & USP).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Rybołowicz (Heriot-Watt University\, UK)
DTSTART:20240408T150000Z
DTEND:20240408T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/64
DESCRIPTION:Title: On affine nature of trusses\nby Bernard Rybołowicz (Heriot-Watt
University\, UK) as part of European Non-Associative Algebra Seminar\n\n\
nAbstract\nIn this presentation\, I will introduce the audience to ternary
algebras called heaps and trusses. Specifically\, I will familiarize the
audience with modules over trusses\, highlighting differences with modules
over rings. The main point will be to show the close relationship between
modules over trusses and affine spaces over rings. I will illustrate that
modules over trusses occupy a position between modules over rings and aff
ine spaces over rings.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paola Stefanelli (University of Salento\, Italy)
DTSTART:20240415T150000Z
DTEND:20240415T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/65
DESCRIPTION:Title: Płonka sums of set-theoretical solutions of the Yang-Baxter equatio
n\nby Paola Stefanelli (University of Salento\, Italy) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nThe Płonka sum is one
of the most significant composition methods in Universal Algebra introduc
ed by Jerzy Płonka in 1967. In particular\, Clifford semigroups have turn
ed out to be the first instances of Płonka sums of groups. In this talk\,
we illustrate a method for constructing set-theoretical solutions of the
Yang-Baxter equation that is inspired by the notion of the Płonka sums. M
oreover\, we will show how to obtain solutions of this type by considering
dual weak braces\, algebraic structures recently studied and described in
a joint work with Francesco Catino and Marzia Mazzotta.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Launois (University of Kent\, UK)
DTSTART:20240422T150000Z
DTEND:20240422T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/66
DESCRIPTION:Title: Derivations of quantum algebras\nby Stéphane Launois (Universi
ty of Kent\, UK) as part of European Non-Associative Algebra Seminar\n\n\n
Abstract\nI will report on joint work in progress with Samuel Lopes and I
saac Oppong where we aim to compute the derivations of quantum nilpotent a
lgebras\, a class on noncommutative algebras which includes in particular
the positive part of quantised enveloping algebras and quantum Schubert ce
lls.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Rowen (Bar-Ilan University\, Israel)
DTSTART:20240506T150000Z
DTEND:20240506T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/68
DESCRIPTION:Title: Weakly primitive axial algebras\nby Louis Rowen (Bar-Ilan Univer
sity\, Israel) as part of European Non-Associative Algebra Seminar\n\n\nAb
stract\nIn earlier work we studied the structure of primitive axial algeb
ras of Jordan type (PAJ's)\, not necessarily commutative\, in terms of the
ir primitive axes. In this paper we weaken primitivity and permit several
pairs of (left and right) eigenvalues satisfying a more general fusion rul
e\, bringing in interesting new examples such as the band semigroup algebr
as and various noncommutative examples. Also we broaden our investigation
to the case of 2-generated algebras for which only one axis satisfies the
fusion rules. As an example we describe precisely the 2-dimensional axial
algebras and the 3-dimensional and 4-dimensional weakly primitive axial
algebras of Jordan type (weak PAJ's)\, and we see\, in contrast to the cas
e for~PAJ's\, that there are higher dimensional weak PAJ's generated by tw
o axes. We also prove a theorem that enables us to reduce weak PAJ's to un
iform components.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Fagundes (University of Campinas\, Brazil)
DTSTART:20240318T150000Z
DTEND:20240318T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/69
DESCRIPTION:Title: The L'vov-Kaplansky conjecture and some of its variations\nby Pe
dro Fagundes (University of Campinas\, Brazil) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nThe L'vov-Kaplansky conjecture cla
ims that the image of a multilinear polynomial on the full matrix algebra
is a vector space. Positive results concerning the conjecture are known on
ly for small cases (polynomials of small degree or matrices of small size)
. Besides presenting the main results on the L'vov-Kaplasnky conjecture\,
in this talk we also will discuss some of its variations such as images of
multilinear polynomials on some subalgebras of the full matrix algebra wi
th additional structure (gradings\, involutions\, graded involutions).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Doikou (Heriot-Watt University\, UK)
DTSTART:20240520T150000Z
DTEND:20240520T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/70
DESCRIPTION:Title: Parametric set-theoretic Yang-Baxter equation: p-racks\, solutions &
quantum algebras\nby Anastasia Doikou (Heriot-Watt University\, UK) a
s part of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe theo
ry of the parametric set-theoretic Yang-Baxter equation is established fro
m a purely algebraic point of view. We introduce generalizations of the f
amiliar shelves and racks named parametric (p)-shelves and racks. These ob
jects satisfy a "parametric self-distributivity" condition and lead to sol
utions of the Yang-Baxter equation. Novel\, non-reversible solutions are
obtained from p-shelve/rack solutions by a suitable parametric twist\, whe
reas all reversible set-theoretic solutions are reduced to the identity ma
p via a parametric twist. The universal algebras associated to both p-rack
and generic parametric set-theoretic solutions are next presented and the
corresponding universal R-matrices are derived. By introducing the conce
pt of a parametric coproduct we prove the existence of a parametric co-ass
ociativity. We show that the parametric coproduct is an algebra homomorphs
im and the universal R-matrices intertwine with the algebra coproducts.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Fioresi (University of Bologna\, Italy)
DTSTART:20240624T150000Z
DTEND:20240624T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/71
DESCRIPTION:Title: Quantum Principal Bundles on Quantum Projective Varieties\nby Ri
ta Fioresi (University of Bologna\, Italy) as part of European Non-Associa
tive Algebra Seminar\n\n\nAbstract\nIn non commutative geometry\, a quantu
m principal bundle over an affine base is recovered through a deformation
of the algebra of its global sections: the property of being a principal b
undle is encoded by the notion of Hopf Galois extension\, while the local
triviality is expressed by the cleft property. We examine the case of a p
rojective base X in the special case X=G/P\, where G is a complex semisimp
le group and P a parabolic subgroup. The quantization of G will then be in
terpreted as the quantum principal bundle on the quantum base space X\, ob
tained via a quantum section.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yvain Bruned (University of Lorraine\, France)
DTSTART:20240527T150000Z
DTEND:20240527T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/72
DESCRIPTION:Title: Novikov algebras and multi-indices in regularity structures\nby
Yvain Bruned (University of Lorraine\, France) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nIn this talk\, we will present mul
ti-Novikov algebras\, a generalisation of Novikov algebras with several bi
nary operations indexed by a given set\, and show that the multi-indices r
ecently introduced in the context of singular stochastic partial different
ial equations can be interpreted as free multi-Novikov algebras. This is p
arallel to the fact that decorated rooted trees arising in the context of
regularity structures are related to free multi-pre-Lie algebras. This is
a joint work with Vladimir Dotsenko.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudemir Fideles (University of Campinas\, Brazil)
DTSTART:20240603T150000Z
DTEND:20240603T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/73
DESCRIPTION:Title: Graded identities in Lie algebras with Cartan gradings: an algorithm
\nby Claudemir Fideles (University of Campinas\, Brazil) as part of Eu
ropean Non-Associative Algebra Seminar\n\n\nAbstract\nThe classification o
f finite-dimensional semisimple Lie algebras in characteristic 0 represent
s one of the significant achievements in algebra during the first half of
the 20th century. This classification was developed by Killing and by Cart
an. According to the Killing–Cartan classification\, the isomorphism cla
sses of simple Lie algebras over an algebraically closed field of characte
ristic zero correspond one-to-one with irreducible root systems. In the in
finite-dimensional case the situation is more complicated\, and the so-cal
led algebras of Cartan type appear. It is somewhat surprising that graded
identities for Lie algebras have been relatively few results to that exten
t. In this presentation\, we will discuss some of the results obtained thu
s far and introduce an algorithm capable of generating a basis for all gra
ded identities in Lie algebras with Cartan gradings. Specifically\, over a
ny infinite field\, we will apply this algorithm to establish a basis for
all graded identities of $U_1$\, the Lie algebra of derivations of the alg
ebra of Laurent polynomials $K[t\,t^{-1}]$]\, and demonstrate that they d
o not admit any finite basis. The findings discussed in this presentation
are joint works with P. Koshlukov (UNICAMP).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erhard Neher (University of Ottawa)
DTSTART:20240610T150000Z
DTEND:20240610T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/74
DESCRIPTION:Title: Corestriction\nby Erhard Neher (University of Ottawa) as part of
European Non-Associative Algebra Seminar\n\n\nAbstract\nCorestriction is
an important technique in the theory of central-simple associative algebra
s over a field. Given a finite étale extension K/F\, e.g. a Galois extens
ion\, corestriction associates a central-simple associative F-algebra with
every central-simple associative K-algebra. In this talk\, I will give an
introduction to corestriction over fields\, applicable to nonassociative
algebras. Towards the end of my talk\, I will indicate why it is of intere
st to generalize corestruction to schemes and sketch how this can be done
(joint work Philippe Gille and Cameron Ruether).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Laubie (University of Strasbourg)
DTSTART:20240617T150000Z
DTEND:20240617T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/75
DESCRIPTION:Title: Combinatorics of free pre-Lie algebras and algebras with several pre
-Lie products sharing the Lie bracket\nby Paul Laubie (University of S
trasbourg) as part of European Non-Associative Algebra Seminar\n\n\nAbstra
ct\nUsing the theory of algebraic operads\, we give a combinatorial descri
ption of free pre-Lie algebras (also known as left-symmetric algebras) wit
h rooted trees. A numerical coincidence hints a similar description for al
gebras with several pre-Lie products sharing the Lie bracket using rooted
Greg trees which are rooted trees with black and white vertices such that
black vertices have at least two children. We then show that those Greg tr
ees can be used to give a description of the free Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andronick Arutyunov (Institute of Control Sciences\, Russia)
DTSTART:20240401T150000Z
DTEND:20240401T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/76
DESCRIPTION:Title: Derivations and other inductive operator families\nby Andronick
Arutyunov (Institute of Control Sciences\, Russia) as part of European Non
-Associative Algebra Seminar\n\n\nAbstract\nDerivations on group algebras
are linear operators. They satisfy the Leibniz rule. Another example are F
ox derivatives\, which satisfy a different (but very similar) identity. We
will give a construction which generalises all such identities and the co
rresponding operator families. The main element of such a construction is
an action groupoid and the space ofcharacters on it. The second step of th
e construction are characters on special graphs (action diagrams) which ar
e equivalent to classical Cayley graphs for the case of left multiplicatio
n action. I will show the way to interpret inner derivations as a special
case of trivial on loops characters. And we will consider a more general i
deal of quasi-inner derivations. These results are based on the author's r
esults\, and the main approach was proposed in collaboration with prof. A.
S. Mischchenko.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Darpö (Linköping University\, Sweden)
DTSTART:20240429T150000Z
DTEND:20240429T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/77
DESCRIPTION:Title: Non-associative algebras in an associative context\nby Erik Darp
ö (Linköping University\, Sweden) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nFor any associative algebra A\, the left regu
lar representation is an embedding of A into its linear endomorphism algeb
ra End(A). In this talk\, I shall explain how this elementary observation
can be generalised to a (less elementary) structure result for general non
-associative algebras. The describes the category of unital\, not necessar
ily associative\, algebras in terms of associative algebras with certain d
istinguished subspaces.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nurlan Ismailov (Astana IT University\, Kazakhstan)
DTSTART:20240701T150000Z
DTEND:20240701T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/78
DESCRIPTION:Title: On variety of right-symmetric algebras\nby Nurlan Ismailov (Asta
na IT University\, Kazakhstan) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nThe problem of the existence of a finite basis of
identities for a variety of associative algebras over a field of characte
ristic zero was formulated by Specht in 1950. We say that a variety of alg
ebras has the Specht property if any of its subvariety has a finite basis
of identities. In 1988\, A. Kemer proved that the variety of associative a
lgebras over a field of characteristic zero has the Specht property. Spech
t’s problem has been studied for many well-known varieties of algebras\,
such as Lie algebras\, alternative algebras\, right-alternative algebras\
, and Novikov algebras. An algebra is called right-symmetric if it satisfi
es the identity (a\, b\, c) = (a\, c\, b) where (a\, b\, c) = (ab)c − a(
bc) is the associator of a\, b\, c. The talk is devoted to the Specht prob
lem for the variety of right-symmetric algebras. It is proved that the var
iety of right-symmetric algebras over an arbitrary field does not satisfy
the Specht property. The talk is based on the results of joint work with U
. Umirbaev.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Lazarev (Lancaster University\, UK)
DTSTART:20240715T150000Z
DTEND:20240715T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/80
DESCRIPTION:Title: Cohomology of Lie coalgebras\nby Andrey Lazarev (Lancaster Unive
rsity\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstr
act\nAssociated to a Lie algebra g and a g-module M is a standard complex
C*(g\,M) computing the cohomology of g with coefficients in M\; this class
ical construction goes back to Chevalley and Eilenberg of the late 1940s.
Shortly afterwards\, it was realized that this cohomology is an example of
a derived functor in the category of g-modules. The Lie algebra g can be
replaced by a differential graded Lie algebra and M – with a dg g-module
with the same conclusion. Later\, a deep connection with Koszul duality
was uncovered in the works of Quillen (late 1960s) and then Hinich (late
1990s). In this talk I will discuss the cohomology of (dg) Lie coalgebras
with coefficients in dg comodules. The treatment is a lot more delicate\,
underscoring how different Lie algebras and Lie coalgebras are (and simila
rly their modules and comodules). A definitive answer can be obtained for
so-called conilpotent Lie coalgebras (though not necessarily conilpotent c
omodules). If time permits\, I will also discuss some topological applicat
ions.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Dokas (National and Kapodistrian University of Athens\, Gr
eece)
DTSTART:20240722T150000Z
DTEND:20240722T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/81
DESCRIPTION:Title: On Quillen-Barr-Beck cohomology for restricted Lie algebras\nby
Ioannis Dokas (National and Kapodistrian University of Athens\, Greece) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this t
alk we define and study Quillen-Barr-Beck cohomology for the category of r
estricted Lie algebras. We prove that the first Quillen-Barr-Beck’s coho
mology classifies general abelian extensions of restricted Lie algebras. M
oreover\, using Duskin-Glenn’s torsors cohomology theory\, we prove a cl
assification theorem for the second Quillen-Barr-Beck cohomology group in
terms of 2-fold extensions of restricted Lie algebras. Finally\, we give a
n interpretation of Cegarra-Aznar’s exact sequence for torsor cohomology
.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Catoire (University of the Littoral Opal Coast\, France)
DTSTART:20240812T150000Z
DTEND:20240812T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/82
DESCRIPTION:Title: The free tridendriform algebra\, Schroeder trees and Hopf algebras\nby Pierre Catoire (University of the Littoral Opal Coast\, France) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe notion
s of dendriform algebras\, respectively tridendriform\, describe the actio
n of some elements of the symmetric groups called shuffle\, respectively q
uasi-shuffle over the set of words whose letters are elements of an alphab
et\, respectively of a monoid. A link between dendriform and tridendriform
algebras will be made. Those words algebras satisfy some properties but t
hey are not free. This means that they satisfy extra properties like commu
tativity. In this talk\, we will describe the free tridendriform algebra.
It will be described with planar trees (not necessarily binary) called Sch
roeder trees. We will describe the tridendriform structure over those tree
s in a non-recursive way. Then\, we will build a coproduct on this algebra
that will make it a (3\, 2)-dendriform bialgebra graded by the number of
leaves. Once it will be build\, we will study this Hopf algebra: duality\,
quotient spaces\, dimensions\, study of the primitives elements...\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Martin-Lyons (Keele University\, UK)
DTSTART:20240902T150000Z
DTEND:20240902T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/83
DESCRIPTION:Title: Skew Bracoids\nby Isabel Martin-Lyons (Keele University\, UK) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe skew
brace was devised by Guanieri and Vendramin in 2017\, building on Rump's b
race. Since then\, the skew brace has been central to the study of solutio
ns to the Yang-Baxter equation\, with connections to many other areas of m
athematics including Hopf-Galois theory. We introduce the skew bracoid\, a
generalisation of the skew brace which can arise as a partial quotient th
ereof. We explore the connection between skew bracoids and Hopf-Galois the
ory\, as well as the more recent connection to solutions of the Yang-Baxte
r equation.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Brzezinski (Swansea University\, UK)
DTSTART:20240513T150000Z
DTEND:20240513T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/84
DESCRIPTION:Title: Lie brackets on affine spaces\nby Tomasz Brzezinski (Swansea Uni
versity\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nWe first explore the definition of an affine space which makes no r
eference to the underlying vector space and then formulate the notion of a
Lie bracket and hence a Lie algebra on an affine space in this framework.
Since an affine space has neither distinguished elements nor additive str
ucture\, the concepts of antisymmetry and Jacobi identity need to be modif
ied. We provide suitable modifications and illustrate them by a number of
examples. The talk is based in part on joint works with James Papworth and
Krzysztof Radziszewski.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Manchon (Clermont Auvergne University\, France)
DTSTART:20240909T150000Z
DTEND:20240909T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/85
DESCRIPTION:Title: Post-Lie algebras\, post-groups and Gavrilov's K-map\nby Dominiq
ue Manchon (Clermont Auvergne University\, France) as part of European Non
-Associative Algebra Seminar\n\n\nAbstract\nPost-Lie algebras appeared in
2007 in algebraic combinatorics\, and independently in 2008 in the study o
f numerical schemes on homogeneous spaces. Gavrilov's K-map is a particula
r Hopf algebra isomorphism\, which can be naturally described in the conte
xt of free post-Lie algebras. Post-groups\, which are to post-Lie algebras
what groups are to Lie algebras\, were defined in 2023 by C. Bai\, L. Guo
\, Y. Sheng and R. Tang. Although skew-braces and braided groups are older
equivalent notions\, their reformulation as post-groups brings crucial ne
w information on their structure. After giving an account of the above-men
tioned structures\, I shall introduce free post-groups\, and describe a gr
oup isomorphism which can be seen as an analogon of Gavrilov's K-map for p
ost-groups. Based on joint work with M. J. H. Al-Kaabi and K. Ebrahimi-Far
d.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Érica Fornaroli (State University of Maringá\, Brazil)
DTSTART:20240729T150000Z
DTEND:20240729T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/86
DESCRIPTION:Title: Involutions of the second kind on finitary incidence algebras\nb
y Érica Fornaroli (State University of Maringá\, Brazil) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nLet K be a field and X
a connected partially ordered set. In this talk we show that the finitary
incidence algebra FI(X\, K) of X over K has an involution of the second k
ind if and only if X has an involution and K has an automorphism of order
2. We also present a characterization of the involutions of the second kin
d on FI(X\, K). We conclude by giving necessary and sufficient conditions
for two involutions of the second kind on FI(X\, K) to be equivalent in th
e case where characteristic of K is different from 2 and every multiplicat
ive automorphism of FI(X\, K) is inner.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuly Billig (Carleton University\, Canada)
DTSTART:20240819T150000Z
DTEND:20240819T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/87
DESCRIPTION:Title: Quasi-Poisson superalgebras\nby Yuly Billig (Carleton University
\, Canada) as part of European Non-Associative Algebra Seminar\n\n\nAbstra
ct\nIn 1985\, Novikov and Balinskii introduced what became known as Noviko
v algebras in an attempt to construct generalizations of Witt Lie algebra.
To their disappointment\, Zelmanov showed that the only simple finite-dim
ensional Novikov algebra is one-dimensional (and corresponds to Witt algeb
ra). The picture is much more interesting in the super case\, where there
are many more generalizations of Witt algebra\, called superconformal Lie
algebras. In 1988 Kac and Van de Leur gave a conjectural list of simple su
perconformal Lie algebras. Their list was amended with a Cheng-Kac superal
gebra\, which was constructed several years later. However\, Novikov super
algebras are not flexible enough to describe all simple superconformal Lie
algebras. In this talk\, we shall present the class of quasi-Poisson alge
bras. Quasi-Poisson algebras have two products: it is a commutative associ
ative (super)algebra\, a Lie (super)algebra\, and has an additional unary
operation\, subject to certain axioms. All known simple superconformal Lie
algebras arise from finite-dimensional simple quasi-Poisson superalgebras
. In this talk\, we shall present basic constructions\, describe the examp
les of quasi-Poisson superalgebras\, and mention some results about their
representations.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Deré (Catholic University of Leuven\, Belgium)
DTSTART:20240826T150000Z
DTEND:20240826T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/88
DESCRIPTION:Title: Simply transitive NIL-affine actions of solvable Lie groups\nby
Jonas Deré (Catholic University of Leuven\, Belgium) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nAlthough not every 1-connec
ted solvable Lie group G admits a simply transitive action via affine maps
on R^n\, it is known that such an action exists if one replaces R^n by a
suitable nilpotent Lie group H\, depending on G. However\, not much is kno
wn about which pairs of Lie groups (G\,H) admit such an action\, where ide
ally you only need information about the Lie algebras corresponding to G a
nd H. In recent work with Marcos Origlia\, we show that every simply trans
itive action induces a post-Lie algebra structure on the corresponding Lie
algebras. Moreover\, if H has nilpotency class 2 we characterize the post
-Lie algebra structures coming from such an action by giving a new definit
ion of completeness\, extending the known cases where G is nilpotent or H
is abelian.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Agore (Free University of Brussels\, Belgium)
DTSTART:20241007T150000Z
DTEND:20241007T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/89
DESCRIPTION:Title: Solutions of the set-theoretic Yang-Baxter equation of Frobenius-Sep
arability (FS) type\nby Ana Agore (Free University of Brussels\, Belgi
um) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe
investigate a special class of solutions of the set-theoretic Yang-Baxter
equation\, called Frobenius-Separability (FS) type solutions. In particula
r\, we show that the category of solutions of the set-theoretic Yang-Baxte
r equation of Frobenius-Separability (FS) type is equivalent to the catego
ry of pointed Kimura semigroups. As applications\, all involutive\, idempo
tent\, nondegenerate\, surjective\, finite order\, unitary or indecomposab
le solutions of FS type are classified. For instance\, if $|X| = n$\, then
the number of isomorphism classes of all such solutions on $X$ that are (
a) left non-degenerate\, (b) bijective\, (c) unitary or (d) indecomposable
and left-nondegenerate is: (a) the Davis number $d(n)$\, (b) $\\sum_{m|n}
\\\, p(m)$\, where $p(m)$ is the Euler partition number\, (c) $\\tau(n) +
\\sum_{d|n}\\left\\lfloor \\frac d2\\right\\rfloor$\, where $\\tau(n)$ is
the number of divisors of $n$\, or (d) the Harary number. The automorphis
m groups of such solutions can also be recovered as automorphism groups $\
\mathrm{Aut}(f)$ of sets $X$ equipped with a single endo-function $f\\colo
n X\\to X$. We describe all groups of the form $\\mathrm{Aut}(f)$ as itera
tions of direct and (possibly infinite) wreath products of cyclic or full
symmetric groups\, characterize the abelian ones as products of cyclic gro
ups\, and produce examples of symmetry groups of FS solutions not of the f
orm $\\mathrm{Aut}(f)$. Based on joint work with A. Chirvasitu and G. Mili
taru.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Feldvoss (University of South Alabama\, USA)
DTSTART:20240916T150000Z
DTEND:20240916T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/90
DESCRIPTION:Title: Semi-simple Leibniz algebras\nby Jörg Feldvoss (University of S
outh Alabama\, USA) as part of European Non-Associative Algebra Seminar\n\
n\nAbstract\nLeibniz algebras were introduced by Blo(c)h in the 1960’s a
nd rediscovered by Loday in the 1990’s as non-anticommutative analogues
of Lie algebras. Many results for Lie algebras have been proven to hold fo
r Leibniz algebras\, but there are also several results that are not true
in this more general context. In my talk\, I will investigate the structur
e of semi-simple Leibniz algebras. In particular\, I will prove a simplici
ty criterion for (left) hemi-semidirect products of a Lie algebra g and a
(left) g-module. For example\, in characteristic zero every finite-dimensi
onal simple Leibniz algebra is such a hemi-semidirect product. But this al
so holds for some infinite-dimensional Leibniz algebras or sometimes in no
n-zero characteristics. More generally\, the structure of finite- dimensio
nal semi-simple Leibniz algebras in characteristic zero can be reduced to
the well-known structure of finite-dimensional semi-simple Lie algebras an
d their finite-dimensional irreducible modules. If time permits\, I will a
pply these structure results to derive some properties of finite-dimension
al semi-simple Leibniz algebras in characteristic zero and other Leibniz a
lgebras that are hemi-semidirect products.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Van Antwerpen (Ghent University\, Belgium)
DTSTART:20240930T150000Z
DTEND:20240930T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/91
DESCRIPTION:Title: Indecomposable and simple solutions of the Yang-Baxter equation\
nby Arne Van Antwerpen (Ghent University\, Belgium) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nRecall that a set-theoretic s
olution of the Yang-Baxter equation is a tuple $(X\,r)$\, where $X$ is a n
on-empty set and $r: X \\times X \\rightarrow X \\times X$ a bijective map
such that $$(r \\times id_X ) (id_X \\times r) (r \\times id_X) = (id_X \
\times r) (r \\times id_X ) (id_X \\times r)\,$$ where one denotes $r(x\,y
)=(\\lambda_x(y)\, \\rho_y(x))$. Attention is often restricted to so-calle
d non-degenerate solutions\, i.e. $\\lambda_x$ and $\\rho_y$ are bijective
. We will call these solutions for short in the remainder of this abstract
. To understand more general objects\, it is an important technique to stu
dy 'minimal' objects and glue these together. For solutions both indecompo
sable and simple solutions fit the bill for being a minimal object. In thi
s talk we will report on recent work with I. Colazzo\, E. Jespers and L. K
ubat on simple solutions. In particular\, we will discuss an extension of
a result of M. Castelli that allows to identify whether a solution is simp
le\, without having to know or calculate all smaller solutions. This metho
d employs so-called skew braces\, which were constructed to provide more e
xamples of solutions\, but also govern many properties of general solution
s. In the latter part of the talk\, we discuss the extension of a method t
o construct new indecomposable or simple solutions from old ones via cabli
ng\, originally introduced by V. Lebed\, S. Ramirez and L. Vendramin to un
ify the known results on indecomposability of solutions.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Łukasz Kubat (University of Warsaw\, Poland)
DTSTART:20240805T150000Z
DTEND:20240805T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/92
DESCRIPTION:Title: On Yang-Baxter algebras\nby Łukasz Kubat (University of Warsaw\
, Poland) as part of European Non-Associative Algebra Seminar\n\n\nAbstrac
t\nTo each solution of the Yang-Baxter equation one may associate a quadra
tic algebra over a field\, called the YB-algebra\, encoding certain inform
ation about the solution. It is known that YB-algebras of finite non-degen
erate solutions are (two-sided) Noetherian\, PI and of finite Gelfand-Kiri
llov dimension. If the solution is additionally involutive then the corres
ponding YB-algebra shares many other properties with polynomial algebras i
n commuting variables (e.g.\, it is a Cohen-Macaulay domain of finite glob
al dimension). The aim of this talk is to explain the intriguing relations
hip between ring-theoretical and homological properties of YB-algebras and
properties of the corresponding solutions of the Yang-Baxter equation. Th
e main focus is on when such algebras are Noetherian\, (semi)prime and rep
resentable. The talk is based on a joint work with I. Colazzo\, E. Jespers
and A. Van Antwerpen.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Garcés (Technical University of Madrid\, Spain)
DTSTART:20240708T150000Z
DTEND:20240708T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/93
DESCRIPTION:Title: Maps preserving the truncation of triple products on Cartan factors<
/a>\nby Jorge Garcés (Technical University of Madrid\, Spain) as part of
European Non-Associative Algebra Seminar\n\n\nAbstract\nWe generalize the
concept of truncation of operators to JB*-triples and study some general p
roperties of bijections preserving the truncation of triple products in b
oth directions between general JB*-triples. In our main result we show tha
t a (non-necessarily linear nor continuous) bijection between atomic JBW*-
triples preserving the truncation of triple products in both directions (a
nd such that the restriction to each rank-one Cartan factor is a continuou
s mapping) is an isometric real linear triple isomorphism.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Chevyrev (University of Edinburgh\, UK)
DTSTART:20241021T150000Z
DTEND:20241021T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/94
DESCRIPTION:Title: Pre-Lie algebras in stochastic PDEs\nby Ilya Chevyrev (Universit
y of Edinburgh\, UK) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nIn this talk\, I will discuss a general method to renormalis
e singular stochastic partial differential equations (SPDEs) using the the
ory of regularity structures. It turns out that\, to derive the renormalis
ed equation\, one can employ a convenient multi-pre-Lie algebra. The pre-L
ie products in this algebra are reminiscent of the pre-Lie product on the
Grossman-Larson algebra of trees\, but come with several important twists.
For the renormalisation of SPDEs\, the important feature of this multi-pr
e-Lie algebra is that it is free in a certain sense. Based on joint work w
ith Yvain Bruned\, Ajay Chandra\, and Martin Hairer.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carla Rizzo (University of Coimbra\, Portugal)
DTSTART:20241111T150000Z
DTEND:20241111T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/95
DESCRIPTION:Title: Differential identities\, almost polynomial growth and matrix algebr
as\nby Carla Rizzo (University of Coimbra\, Portugal) as part of Europ
ean Non-Associative Algebra Seminar\n\n\nAbstract\nLet $F$ be a field of c
haracteristic zero\, $L$ a Lie algebra over $F$\, and $A$ an $L$-algebra -
that is\, an associative algebra over $F$ with an action of $L$ induced b
y derivations. This action of $L$ on $A$ can be extended to an action of i
ts universal enveloping algebra $U(L)$\, leading to the concept of $L$-ide
ntities or differential identities of $A$: polynomials in variables $x^u :
= u(x)$\, where $u \\in U(L)$\, that vanish under all substitutions of ele
ments from $A$. Differential identities were first introduced by Kharchenk
o in 1978\, and\, in later years\, subsequent work by Gordienko and Kochet
ov has spurred a renewed interest in both their structure and quantitative
properties. In this talk\, I will present recent results on the different
ial identities of matrix $L$-algebras\, with a particular focus on their c
lassification and growth behavior.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Fernández (Technical University of Madrid\, Spain)
DTSTART:20241202T150000Z
DTEND:20241202T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/96
DESCRIPTION:Title: Noncommutative Poisson geometry and pre-Calabi-Yau algebras\nby
David Fernández (Technical University of Madrid\, Spain) as part of Europ
ean Non-Associative Algebra Seminar\n\n\nAbstract\nIn order to define suit
able noncommutative Poisson structures\, M. Van den Bergh introduced doubl
e Poisson algebras and double quasi-Poisson algebras. Furthermore\, N. Iyu
du and M. Kontsevich found an insightful correspondence between double Poi
sson algebras and pre-Calabi-Yau algebras\; certain cyclic A∞-algebras w
hich can be seen as noncommutative versions of shifted Poisson manifolds.
In this talk I will present an extension of the Iyudu-Kontsevich correspon
dence to the differential graded setting. I will also explain how double q
uasi-Poisson algebras give rise to pre-Calabi-Yau algebras. This is a join
t work with E. Herscovich (EPFL).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Tocino Sánchez (University of Málaga\, Spain)
DTSTART:20241216T150000Z
DTEND:20241216T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/97
DESCRIPTION:Title: Tensor product of evolution algebras\nby Alicia Tocino Sánchez
(University of Málaga\, Spain) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nThe starting point of this talk is the fact that
the class of evolution algebras over a fixed field is closed under tensor
product. We prove that\, under certain conditions\, the tensor product is
an evolution algebra if and only if every factor is an evolution algebra.
Another issue arises about the inheritance of properties from the tensor p
roduct to the factors and conversely. For instance\, nondegeneracy\, irred
ucibility\, perfectness and simplicity are investigated. The four-dimensio
nal case is illustrative and useful to contrast conjectures\, so we achiev
e a complete classification of four-dimensional perfect evolution algebras
emerging as tensor product of two-dimensional ones. We find that there ar
e four-dimensional evolution algebras that are the tensor product of two n
onevolution algebras. This is a joint work together with Yolanda Cabrera C
asado\, Dolores Martín Barquero and Cándido Martín González.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raschid Abedin (ETH Zürich\, Switzerland)
DTSTART:20241028T150000Z
DTEND:20241028T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/98
DESCRIPTION:Title: Classification of D-bialgebras via algebraic geometry\nby Raschi
d Abedin (ETH Zürich\, Switzerland) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nIn a now classic paper\, Belavin and Drinfel
d categorized solutions to the classical Yang-Baxter equation (CYBE)\, an
equation crucial to the theory of integrable systems\, into three classes:
elliptic\, trigonometric and rational. It is possible to reproduce this r
esult by geometrizing solutions of the CYBE and then applying algebro-geom
etric methods. In this talk\, we will explain how this approach can be use
d to categorize Lie bialgebra structures on power series Lie algebras\, as
well as non-associative generalizations of these structures: D-bialgebra
structures on more general power series algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar León Sánchez (University of Manchester\, UK)
DTSTART:20241209T150000Z
DTEND:20241209T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/99
DESCRIPTION:Title: A basis theorem for Poisson algebras coming from infinite dimensiona
l Lie algebras\nby Omar León Sánchez (University of Manchester\, UK)
as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nI will
present joint work with Sue Sierra where we proved the ACC for radical Po
isson ideals of the symmetric algebra of a Dicksonian Lie algebra. Part of
the talk will be devoted to explaining what Dicksonian means (and give a
variety of examples)\, and then discuss the method of proof of the basis t
heorem. We will observe why our result applies to graded-simple Lie algebr
as.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slaven Kožić (University of Zagreb\, Croatia)
DTSTART:20241014T150000Z
DTEND:20241014T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/100
DESCRIPTION:Title: Representations of the quantum affine vertex algebra associated wi
th the trigonometric $R$-matrix of type $A$\nby Slaven Kožić (Univer
sity of Zagreb\, Croatia) as part of European Non-Associative Algebra Semi
nar\n\n\nAbstract\nOne important problem in the vertex algebra theory is
to associate certain vertex algebra-like objects\, the quantum vertex al
gebras\, to\nvarious classes of quantum groups\, such as quantum affine al
gebras or double Yangians.\nIn this talk\, I will discuss this proble
m in the context of Etingof--Kazhdan's quantum affine vertex algebra $\\ma
thcal{V}^c(\\mathfrak{gl}_N)$ associated with the trigonometric $R$-matri
x of type $A$. \nThe main focus will be on the explicit description of th
e center of $\\mathcal{V}^c(\\mathfrak{gl}_N)$ at the critical level $c=-N
$ and\, furthermore\, on the connection between certain classes of $\\math
cal{V}^c(\\mathfrak{gl}_N)$-modules and representation theories of the qua
ntum affine algebra of type $A$ and the orthogonal twisted $h$-Yangian. Th
e talk is in part based on the joint works with Alexander Molev and Lucia
Bagnoli.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Bajo (University of Vigo\, Spain)
DTSTART:20240923T150000Z
DTEND:20240923T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/101
DESCRIPTION:Title: Quadratic Lie algebras admitting 2-plectic structures\nby Ignac
io Bajo (University of Vigo\, Spain) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nA 2-plectic form ω on a Lie algebra is a 3-
form on the algebra such that it is closed and non-degenerate in the sense
that\, for every nonzero x\, the bilinear form ω(x\, ·\, ·) is not ide
ntically zero. We will study the existence of 2-plectic structures on the
so-called quadratic Lie algebras\, which are Lie algebras admitting an ad-
invariant pseudo-Euclidean product. It is well-known that every centerless
quadratic Lie algebra admits a 2-plectic form but not many quadratic exam
ples with nontrivial center are known. We give several constructions to ob
tain large families of 2-plectic quadratic Lie algebras with nontrivial ce
nter\, many of them among the class of nilpotent Lie algebras. We give som
e sufficient conditions to assure that certain extensions of 2-plectic qua
dratic Lie algebras result to be 2-plectic as well. For instance\, we show
that oscillator algebras can be naturally endowed with 2-plectic structur
es. We prove that every quadratic and symplectic Lie algebra with dimensio
n greater than 4 also admits a 2-plectic form. Further\, conditions to ass
ure that one may find a 2-plectic which is exact on certain quadratic Lie
algebras are obtained.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Montaner (University of Zaragoza\, Spain)
DTSTART:20241104T150000Z
DTEND:20241104T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/102
DESCRIPTION:Title: Pairs of quotients of Jordan pairs\nby Fernando Montaner (Unive
rsity of Zaragoza\, Spain) as part of European Non-Associative Algebra Sem
inar\n\n\nAbstract\nIn this talk we expose ongoing joint work with I Panie
llo on systems of quotients (in a sense partially extending the localizati
on theory of Jordan algebras\, which in turn is inspired by the localizati
on theory of associative algebras). Localization theory in associative alg
ebras originated in the purpose of extending the construction of fields of
quotients of integral domains\, and therefore in the purpose of defining
ring extensions in which a selected set of elements become invertible. As
it is well known in associative theory that led to Goldie's theorems\, a
nd these in turn to more general localization theories for which the denom
inators of the fraction-like elements of the extensions are (one-sided) id
eals taken in a class of filters (Gabriel filters). These ideas have been
partially extended to Jordan algebras by several authors (starting with Ze
lmanov's version of Goldie theory in the Jordan setting\, and its extensio
n by Fernandez López-García Rus and Montaner) and Paniello and Montaner
(among others) definition of algebras of quotients of Jordan algebras. Fol
lowing the development of Jordan theory\, a natural direction for extendin
g these results is considering the context of Jordan pairs. This is the ob
jective of the research presented here. Since obviously a Jordan pair cann
ot have invertible elements unless it is an algebra\, and in this case we
are back in the already developed theory\, the kind of quotients that woul
d make a significative (proper) extension of the case of algebras should b
e based in a different notion of quotient. An approach that seems to be p
romising is considering the Jordan extension of Fountain and Gould notion
of local order\, as has been adapted to Jordan algebras by the work of Fer
nández López\, and more recently by Montaner and Paniello with the notio
n of local order\, in which the bridge between algebras and pairs is estab
lished by local algebras following the ideas of D'Amour and McCrimmon. In
the talk this idea is exposed\, together with the state of the research\,
and the open problems that it raises.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos André (University of Lisboa\, Portugal)
DTSTART:20241125T150000Z
DTEND:20241125T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/103
DESCRIPTION:Title: Supercharacters of adjoint groups of radical rings and related subg
roups\nby Carlos André (University of Lisboa\, Portugal) as part of E
uropean Non-Associative Algebra Seminar\n\n\nAbstract\nDescribing the conj
ugacy classes and/or irreducible characters of the unitriangular group ove
r a finite field is known to be an impossibly difficult problem. Superclas
ses and supercharacters have been introduced (under the names of "basic va
rieties" and "basic characters") as an attempt to approximate conjugacy cl
asses and irreducible characters using a cruder version of Kirillov's meth
od of coadjoint orbits.\n\nIn the past thirty years\, these notions have b
een recognised in several areas (seemingly unrelated to representation the
ory): exponential sums in number theory\, random walks in probability and
statistics\, association schemes in algebraic combinatorics...\n\nIn this
talk\, we will describe and illustrate the main ideas and recent developme
nts of the standard supercharacter theory of adjoint groups of radical rin
gs. We will explore the close relation to Schur rings\, and extend a well-
known factorisation of supercharacters of unitriangular groups which expla
ins the alternative definition as basic characters.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Zadunaisky (University of Buenos Aires\, Argentina)
DTSTART:20241118T150000Z
DTEND:20241118T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/104
DESCRIPTION:Title: Clebsch-Gordan revisited\nby Pablo Zadunaisky (University of Bu
enos Aires\, Argentina) as part of European Non-Associative Algebra Semina
r\n\n\nAbstract\nBy an ultra classical result\, the tensor product of a si
mple representation of gl(n\,C) and its defining representation decomposes
as a direct sum of simple representations without multiplicities. This me
ans that for each highest weight\, the space of highest weight vectors is
one dimensional. We will give an explicit construction of these highest we
ight vectors\, and show that they arise from the action of certain element
s in the enveloping algebra of gl(n\,c)+gl(n\,C) on the tensor product. Th
ese elements are independent of the simple representation we started with\
, and in fact produce highest weight vectors in several other contexts. (J
oint with Joanna Meinel from Bonn University)\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (University of Manchester\, UK)
DTSTART:20250106T150000Z
DTEND:20250106T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/105
DESCRIPTION:Title: Geometric rigidity of modules for algebraic groups\nby David St
ewart (University of Manchester\, UK) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nLet k be a field\, let G be a smooth affine
k-group of finite type\, and V a finite-dimensional G-module. We say V is
rigid if the socle series and radical series coincide for the action of G
on each indecomposable summand of V\; say V is geometrically rigid (resp.
absolutely rigid) if V is rigid after base change of G and V to an algebr
aic closure of k (resp. any field extension of k). We show that all simple
G-modules are geometrically rigid\, though they are not in general absolu
tely rigid. More precisely\, we show that if V is a simple G-module\, then
there is a finite purely inseparable extension k_V /k naturally attached
to V such that V_{k_V} is absolutely rigid as a G_{k_V} -module. The proof
for connected G turns on an investigation of algebras of the form K \\oti
mes_k E where K and E are field extensions of k\; we give an example of su
ch an algebra which is not rigid as a module over itself. We establish the
existence of the purely inseparable field extension k_V /k through an ana
logous version for Artinian algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Millionshchikov (Lomonosov University\, Russia)
DTSTART:20250113T150000Z
DTEND:20250113T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/106
DESCRIPTION:Title: Narrow Lie (super)algebras\nby Dmitry Millionshchikov (Lomonoso
v University\, Russia) as part of European Non-Associative Algebra Seminar
\n\n\nAbstract\nWe discuss narrow in the sense of Shalev and Zelmanov posi
tively graded Lie (super)algebras. They appear in different problems of ge
ometry\, topology and math physics. We will pay attention to the classific
ation results as well as to the applications.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Mancini (University of Palermo\, Italy)
DTSTART:20250120T150000Z
DTEND:20250120T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/107
DESCRIPTION:Title: On the representability of actions of non-associative algebras\
nby Manuel Mancini (University of Palermo\, Italy) as part of European Non
-Associative Algebra Seminar\n\n\nAbstract\nIt is well known that in the s
emi-abelian category Grp of groups\, split extensions\, or equivalently in
ternal actions\, are represented by automorphisms. This means that the cat
egory Grp is action representable and the actor of a group X is the group
Aut(X). The notion of action representable category has proven to be quite
restrictive: for instance\, if a non-abelian variety of non-associative a
lgebras\, over an infinite field of characteristic different from two\, is
action representable\, then it is the category of Lie algebras. More rece
ntly G. Janelidze introduced the notion of weakly action representable cat
egory\, which includes a wider class of categories. In this talk we show t
hat for an algebraically coherent variety of algebras and an object X of i
t\, it is always possible to construct a partial algebra E(X)\, called ext
ernal weak actor of X\, which allows us to describe internal actions on X.
Moreover\, we show that the existence of a weak representation is connect
ed to the amalgamation property\, and we give an application of the constr
uction of the external weak actor in the context of varieties of unitary a
lgebras. This is joint work with J. Brox\, (Universidad de Valladolid)\, X
abier García Martínez (Universidade de Vigo)\, Tim Van der Linden and Co
rentin Vienne (Université catholique de Louvain).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Stasenko (HSE University\, Russia)
DTSTART:20250127T150000Z
DTEND:20250127T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/108
DESCRIPTION:Title: Short $SL_2$-structures on simple Lie algebras and Lie's modules\nby Roman Stasenko (HSE University\, Russia) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nLet $S$ be an arbitrary reductive
algebraic group. Let's call a homomorphism $\\Phi:S\\rightarrow\\operator
name{Aut}(\\mathfrak{g})$ an {\\it $S$-structure on the Lie algebra $\\mat
hfrak{g}$}. $S$-structures were previously invetigated by various authors\
, including E.B. Vinberg. The talk deals with $SL_2$-structures. Let's cal
l the $SL_2$-structure short if the representation $\\Phi$ of the group $S
L_2$ decomposes into irreducible representations of dimensions 1\, 2 and 3
. If we consider irreducible representations of dimensions only 1 and 3\,
we get the well-known Tits-Kantor-Koeher construction\, which establishes
a one-to-one correspondence between simple Jordan algebras and simple Lie
algebras of a certain type. Similarly to the Tits–Kantor–Koeher theore
m\, in the case of short $SL_2$-structures\, there is a one-to-one corresp
ondence between simple Lie algebras with such a structure and the so-call
ed simple symplectic Lie-Jordan structures. Let $\\mathfrak{g}$ be a Lie
algebra with $SL_2$-structure and the map $\\rho:\\mathfrak{g}\\rightarrow
\\mathfrak{gl}(U)$ be linear representation of $\\mathfrak{g}$. The homoph
ism $\\Psi:S\\rightarrow GL(U)$ is called a $SL_2$-structure on the Lie $\
\mathfrak{g}$-module $U$ if $$\\Psi(s)\\rho(\\xi)u =\\rho(\\Phi(s)\\xi)\\P
si(s)u\,\\quad\\forall s\\in S\, \\xi\\in\\mathfrak{g}\, u\\in U.$$ This c
onstrution has interesting applications to the representation theory of Jo
rdan algebras\, which will be discussed during the talk. We will also pres
ent a complete classification of irreducible short $\\mathfrak{g}$-modules
for simple Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lina Oliveira (IST University of Lisboa\, Portugal)
DTSTART:20250203T150000Z
DTEND:20250203T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/109
DESCRIPTION:Title: Tits–Kantor–Koecher Lie algebras and their representations\
nby Lina Oliveira (IST University of Lisboa\, Portugal) as part of Europea
n Non-Associative Algebra Seminar\n\n\nAbstract\nThis talk is an introduct
ion to the Tits–Kantor–Koecher Lie algebras associated with Jordan tri
ples. In particular\, we will obtain representations of these algebras as
matrix Lie algebras. The necessary background will be provided\, as to ren
der the talk self-contained.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Sciandra (University of Turin\, Italy)
DTSTART:20250210T150000Z
DTEND:20250210T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/110
DESCRIPTION:Title: Yetter—Drinfeld post-Hopf algebras and Yetter—Drinfeld relative
Rota—Baxter operators\nby Andrea Sciandra (University of Turin\, It
aly) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nRe
cently\, Li\, Sheng and Tang introduced post-Hopf algebras and relative Ro
ta—Baxter operators (on cocommutative Hopf algebras)\, providing an adju
nction between the respective categories under the assumption that the str
uctures involved are cocommutative. We introduce Yetter— Drinfeld post-H
opf algebras\, which become usual post-Hopf algebras in the cocommutative
setting. In analogy with the correspondence between cocommutative post-Hop
f algebras and cocommutative Hopf braces\, the category of Yetter—Drinfe
ld post-Hopf algebras is isomorphic to the category of Yetter—Drinfeld b
races\, introduced by the author in a joint work with D. Ferri. The latter
structures are equivalent to matched pairs of actions on Hopf algebras an
d generalise both Hopf braces and Majid’s transmutation. We also prove t
hat the category of Yetter—Drinfeld post-Hopf algebras is equivalent to
a subcategory of Yetter—Drinfeld relative Rota—Baxter operators (that
generalise bijective relative Rota—Baxter operators on cocommutative Hop
f algebras). Once the surjectivity of the latter operators is removed\, th
e equivalence is replaced by an adjunction and one recovers\, in the cocom
mutative case\, the result of Li\, Sheng and Tang. The talk is partially b
ased on a joint work with D. Ferri.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Blachar (Bar-Ilan University\, Israel)
DTSTART:20250217T150000Z
DTEND:20250217T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/111
DESCRIPTION:Title: Semiassociative algebras over a field\nby Guy Blachar (Bar-Ilan
University\, Israel) as part of European Non-Associative Algebra Seminar\
n\n\nAbstract\nAssociative central simple algebras are a classical subject
\, related to many areas of study including Galois cohomology and algebrai
c geometry. An associative central simple algebra is a form of matrices be
cause a maximal étale subalgebra acts on the algebra faithfully by left a
nd right multiplication. In an attempt to extract and isolate the full pot
ential of this point of view\, we study nonassociative algebras whose nucl
eus contains an étale subalgebra bi-acting faithfully on the algebra. We
show that these algebras\, termed semiassociative\, are forms of a nonasso
ciative analogue of matrix algebras. Finally\, we consider the monoid comp
osed of semiassociative algebras modulo the nonassociative matrix algebras
\, and discuss its connection to the classical Brauer group. Based on join
t work with Darrell Haile\, Eliyahu Matzri\, Edan Rein and Uzi Vishne.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Vrije Universiteit Brussel\, Belgium)
DTSTART:20250224T150000Z
DTEND:20250224T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/112
DESCRIPTION:Title: Nichols Algebras over groups\nby Leandro Vendramin (Vrije Unive
rsiteit Brussel\, Belgium) as part of European Non-Associative Algebra Sem
inar\n\n\nAbstract\nNichols algebras appear in several areas of mathematic
s\, from Hopf algebras and quantum groups to Schubert calculus and conform
al field theories. In this talk\, I will review the main problems related
to finite-dimensional Nichols algebras over groups and discuss a very rece
nt classification theorem written in collaboration with Andruskiewitsch an
d Heckenberger.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loïc Foissy (University of the Littoral Opal Coast\, France)
DTSTART:20250303T150000Z
DTEND:20250303T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/113
DESCRIPTION:Title: Double bialgebra of noncrossing partitions\nby Loïc Foissy (Un
iversity of the Littoral Opal Coast\, France) as part of European Non-Asso
ciative Algebra Seminar\n\n\nAbstract\nA double bialgebra is a family $(A\
,m\,\\Delta\,\\delta)$ such that both $(A\,m\,\\Delta)$ and $(A\,m\,\\delt
a)$ are bialgebras\, with the extra condition that seeing $\\delta$ as a r
ight coaction on itself\, $m$ and $\\Delta$ are right comodules morphism o
ver $(A\,m\,\\delta)$. A classical example is given by the polynomial alge
bra $\\mathbb{C}[X]$\, with its two classical coproducts. In this talk\, w
e will present a double bialgebra structure on the symmetric algebra gener
ated by noncrossing partitions. The first coproduct is given by the separa
tions of the blocks of the partitions\, with respect to the entanglement\,
and the second one by fusions of blocks. This structure implies that ther
e exists a unique polynomial invariant on noncrossing partitions which res
pects both coproducts: we will give some elements on this invariant\, and
applications to the antipode of noncrossing partitions.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (University of Turin\, Italy)
DTSTART:20250317T150000Z
DTEND:20250317T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/114
DESCRIPTION:Title: Special Hermitian metrics on solvable Lie algebras\nby Anna Fin
o (University of Turin\, Italy) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nI will present recent results on the existence of
SKT and balanced metrics on solvable Lie algebras. The talk is based on
joint papers with Beatrice Brienza\, Asia Mainenti and Fabio Paradiso.\
n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Sorbonne Paris North University\, France)
DTSTART:20250324T150000Z
DTEND:20250324T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/115
DESCRIPTION:Title: Homotopy bialgebraic structures in geometry and topology\nby Br
uno Vallette (Sorbonne Paris North University\, France) as part of Europea
n Non-Associative Algebra Seminar\n\n\nAbstract\nIt is well known from the
PhD thesis of Jim Stasheff that the homotopy theory of associative algebr
as is encoded by homotopy associative algebras\, aka A_infini-algebras\, s
ince this latter notion carries infini-morphisms and satisfies a homotopy
transfer theorem\, for instance. A_infini-algebra structures encode the to
pological data of a space on the level of cochain complexes. When one want
s to encode more data\, like the Poincaré duality of manifolds\, string t
opology\, or non-commutative derived geometry\, then one has to consider f
urther structural operations\, like symmetric bitensors or double brackets
. The purpose of this talk will be to present the associated new types of
homotopy bialgebras\, to explain their relationship\, and to show that the
y admit suitable homotopy properties like infini-morphisms and homotopy tr
ansfer theorem. To mention them\, we will treat pre-Calabi—Yau algebras\
, homotopy double Poisson bialgebras\, and homotopy infinitesimal balanced
bialgebras. This is based on a joint work with Johan LERAY available at a
rXiv:2203.05062.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Paris Cité University\, France)
DTSTART:20250331T150000Z
DTEND:20250331T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/116
DESCRIPTION:Title: From Coxeter-Conway friezes to cluster algebras\nby Bernhard Ke
ller (Paris Cité University\, France) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nSince their invention by Fomin-Zelevinsky
in 2002\, cluster algebras have shown up in an ever growing array of subje
cts in mathematics (and in physics). In this talk\, we will approach their
theory starting from elementary examples. More precisely\, we will see ho
w the remarkable integrality properties of the Coxeter-Conway friezes and
the Somos sequence find a beautiful unification and generalization in Fomi
n-Zelevinsky's definition of cluster variables and their Laurent phenomeno
n theorem. Motivated by the periodicity of Coxeter-Conway friezes\, we wil
l conclude with a general periodicity theorem\, whose proof is based on th
e interaction between discrete dynamical systems and quiver representation
s through the combinatorial framework of cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jari Desmet (Ghent University\, Belgium)
DTSTART:20250407T150000Z
DTEND:20250407T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/117
DESCRIPTION:Title: Jordan algebras and automorphism groups of Matsuo algebras\nby
Jari Desmet (Ghent University\, Belgium) as part of European Non-Associati
ve Algebra Seminar\n\n\nAbstract\nPrimitive axial algebras of Jordan type
half were introduced by Jonathan Hall\, Felix Rehren and Sergey Shpectorov
in 2015\, generalizing Jordan algebras by requiring that their idempotent
s satsify the Peirce decomposition. More specifically\, primitive axial al
gebras of Jordan type $\\frac{1}{2}$ are commutative non-associative algeb
ras generated by idempotents $a$ such that their multiplication operators
$L_a$ are diagonalizable with eigenvalues $\\{1\,0\,\\frac{1}{2}\\}$\, suc
h that the fusion laws $V_1 = \\langle a\\rangle$\, $V_0^2 \\subseteq V_0$
\, $V_0V_{\\frac{1}{2}} \\subseteq V_{\\frac{1}{2}}$ and $V_{\\frac{1}{2}}
^2 \\subseteq V_0 \\oplus V_1$ hold\, where $V_\\lambda$ is the $\\lambda$
-eigenspace of $L_a$. The most well-known examples of this class of algebr
as are either Jordan algebras or Matsuo algebras\, certain non-assocative
algebras related to 3-transposition groups that Atsushi Matsuo discovered
while studyin vertex operator algebras. In this talk\, we will sketch how
one can distinguish these two classes in terms of their automorphism group
s. In particular\, primitive axial algebras of Jordan type half with large
automorphism groups are automatically Jordan while the automorphism group
s of non-Jordan Matsuo algebras are usually finite\, with one infinite fam
ily of exceptions.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Blecher (University of Houston\, USA)
DTSTART:20250310T150000Z
DTEND:20250310T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/118
DESCRIPTION:Title: Jordan operator algebras and beyond\nby David Blecher (Universi
ty of Houston\, USA) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nWe discuss the class of Jordan operator algebras\, including
reporting on recent progress on their M-ideals (joint with M. Neal\, A. P
eralta \, S. Su). More generally we consider some nonassociative algebra
s motivated by Hilbert space operator algebraic theory and group represent
ations.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanna Carnovale (University of Padua\, Italy)
DTSTART:20250414T150000Z
DTEND:20250414T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/119
DESCRIPTION:Title: Nichols algebras over simple groups\nby Giovanna Carnovale (Uni
versity of Padua\, Italy) as part of European Non-Associative Algebra Semi
nar\n\n\nAbstract\nNichols (small shuffle) algebras are a family of graded
algebras including the symmetric algebras\, the exterior algebras\, the p
ositive part of quantized enveloping algebras. They are defined by genera
tors and relations that depend on a vector space V and a solution of the b
raid equation on V\\otimes V. A subclass of them\, which is relevant for t
he classification program of finite-dimensional Hopf algebras developed by
Andruskiewitsch and Schneider\, consists of those for which the solution
of the braid equation stems from a suitable graded representation of a fin
ite group G. A folklore conjecture states that there are no non-trivial fi
nite-dimensional Nichols algebras in this family if G is a non-abelian sim
ple group. I will report on progress on this conjecture\, based on a colla
borations with N. Andruskiewitsch\, G. García and M. Costantini.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kotchetov (Memorial University\, Canada)
DTSTART:20250421T150000Z
DTEND:20250421T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/120
DESCRIPTION:Title: Almost fine gradings on algebras and classification of gradings up
to isomorphism\nby Mikhail Kotchetov (Memorial University\, Canada) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nSince the
works of Patera-Zassenhaus (1989) and Bahturin-Sehgal-Zaicev (2001)\, the
problem of classifying gradings by groups on various algebras has receive
d much attention. There are typically two kinds of classification of gradi
ngs on a given algebra A: fine gradings up to equivalence or all G-grading
s\, for a fixed group G\, up to isomorphism. These classifications are rel
ated\, but it is not straightforward to pass from one to the other. In thi
s talk\, based on a recent paper with A. Elduque\, we introduce a class of
gradings\, which we call almost fine\, on a finite-dimensional algebra A
over an algebraically closed field\, such that every G-grading on A is obt
ained from an almost fine grading in an essentially unique way (which is n
ot the case with fine gradings). For abelian groups\, we give a method of
obtaining all almost fine gradings if fine gradings are known. If time per
mits\, we will illustrate this approach in the case of simple Lie algebras
in characteristic 0: to any abelian group grading with nonzero identity c
omponent\, we attach a (possibly nonreduced) root system Φ and construct
an adapted Φ-grading.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Ignatyev (HSE University\, Russia)
DTSTART:20250428T150000Z
DTEND:20250428T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/121
DESCRIPTION:Title: Tangent cones to Schubert varieties form Kac--Moody groups\nby
Mikhail Ignatyev (HSE University\, Russia) as part of European Non-Associa
tive Algebra Seminar\n\n\nAbstract\nStudying of the geometry of Schubert v
arieties for simple algebraic finite-dimensional complex groups is a class
ical topic in algebraic geometry. Tangent cones encode a lot of geometric
information about singularity of Schubert varieties. One of the very impor
tant tool in investigation properties of tangent cones are Kostant--Kumar
polynomials. I will discuss how this topics can be generalized to the case
of Kac--Moody groups.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Janssens (Catholic University of Louvain\, Belgium)
DTSTART:20250505T150000Z
DTEND:20250505T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/122
DESCRIPTION:Title: On the loop Hecke algebra\nby Geoffrey Janssens (Catholic Unive
rsity of Louvain\, Belgium) as part of European Non-Associative Algebra Se
minar\n\n\nAbstract\nTo any braid group $B_n$ there is an associated (
Iwahori-)Hecke algebra $H_q (n)$. Over time this algebra has shown to
be as intriguing as $B_n$. For example\, $H_q (n)$ possesses a represe
ntation for which it is in a Schur–Weyl relation with $U_q (sl_d). O
ne possible interpretation of classical braid groups is as a fundamental g
roup of the space of configurations of $n$ distinct points in $R^2$. Taki
ng this motion group perspective\, it is natural to consider configuration
s of $n$ unit circles $S^1$. This yields the so-called Loop Braid group. D
amiani–Martin–Rowell associated an analogue of the Hecke algebra and m
ade a conjecture on the dimension of this Loop Hecke algebra. In this talk
we will firstly briefly introduce the mentioned objects and subsequently
tell about how the above Schur–Weyl picture adapts to the Loop setting.
In the last part of the talk we will discuss the simple representations an
d the Jacobson radical.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sue Sierra (University of Edinburgh\, UK)
DTSTART:20250519T150000Z
DTEND:20250519T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/123
DESCRIPTION:Title: Ideals of enveloping algebras of loop algebras\nby Sue Sierra (
University of Edinburgh\, UK) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nLet g be a finite-dimensional simple Lie algebra\,
and consider the loop algebra $L_g = g[t\, t^{-1}]$ and the affine Lie alg
ebra $\\hat{g}$\, which is an extension of $L_g$ by a central element $c$.
We investigate two-sided ideals in the universal enveloping algebra $U(L_
g)$. It is known that the rings $U(\\hat{g})/(c-\\lambda)$ are simple for
any nonzero scalar $\\lambda$\, but the two-sided structure of $U(L_g) =
U(\\hat{g}/(c))$ is more complicated. We show that $U(L_g)$ does not sati
sfy the ascending chain condition on two-sided ideals\, but that the two-s
ided ideals still have a nice structure: there is a canonical collection o
f ideals $I_n$\, parameterised by positive integers\, so that any two-side
d ideal of $U(L_g)$ contains some $I_n$. The ideals $I_n$ can be thought
of as universal annihilators of classes of finite-dimensional representati
ons of $L_g$. This is a preliminary report on joint work with Alexey Petuk
hov.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Young (University of Hertfordshire\, UK)
DTSTART:20250512T150000Z
DTEND:20250512T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/124
DESCRIPTION:Title: Higher current algebras and chiral algebras\nby Charles Young (
University of Hertfordshire\, UK) as part of European Non-Associative Alge
bra Seminar\n\n\nAbstract\nVertex algebras capture physicists' notion of O
PEs in chiral CFTs\, in complex dimension one. For various motivations\, o
ne would like to have analogs of vertex algebras in higher dimensions. Chi
ral algebras\, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory\,
provide a promising framework here\, because they re-express the vertex al
gebra axioms (which are rather sui generis\, and therefore hard to general
ize) as something more recognizable (a chiral algebra is a Lie algebra\, o
f a sort).\n\nI will review this\, and then go on to introduce a certain c
oncrete model of the unit chiral algebra in higher complex dimensions. We
shall see that in going to higher dimensions\, one naturally moves from Li
e algebras to their homotopy analogs\, L-infinity algebras\, and from chir
al algebras to homotopy chiral algebras in a sense recently introduced by
Malikov-Schechtman. The main tool in the talk will be a new model -- the p
olysimplicial model -- of derived sections of the sheaf of functions on hi
gher configuration spaces. The hope is that this model will prove well-ada
pted to doing concrete calculations.\n\nThis is joint work in preparation
with Zhengping Gui and Laura Felder.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Farinati (University of Buenos Aires\, Argentina)
DTSTART:20250602T150000Z
DTEND:20250602T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/125
DESCRIPTION:Title: The Tits construction for SHORT $\\mathfrak{sl}_2$-super-structures
.\nby Marco Farinati (University of Buenos Aires\, Argentina) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nWhen we have an
action of $\\mathfrak{sl}_2$ on a given structure\, one may decompose it
on its isotypic components. More concretely\, if $A$ is a finite dimension
al "algebra" with an operation $m:A\\otimes A\\to A$\, one may decompose $
A=\\oplus_n V_n\\otimes M_n$\, where $V_n$ is the irreducible $\\mathfrak{
sl}_2$-module of highest weight $n$ (and dimension $n+1$) and $M_n$ is jus
t a "multiplicity" vector space. If the operation $m$ is $\\mathfrak{sl}_2
$-linear\, then\, a priori\, several restrictions for the operation $m$ c
an be deduced\, and algebraic identities (e.g. associativity\, Jacobi iden
tity\, symmetry\, antisymmetry\,...) of $A$ can be translated into operati
ons and identities on the $M_n$'s.\n\nIn case the only isotypical componen
ts that appear are the trivial ($V_0$) and the adjoint ($V_2$)\, then the
$\\mathfrak{sl}_2$ structure is called VERY SHORT. In case the only isotyp
ical components that appear are the trivial ($V_0$)\, the adjoint ($V_2$)\
, and the defining 2-dimensional representation ($V=\\mathcal{C}^2=V_1$) t
hen the $\\mathfrak{sl}_2$ structure is called SHORT.\n\nThe case of VERY
SHORT $\\mathfrak{sl}_2$ Lie algebras is a classical object studied by Tit
s and leads to Jordan algebras. There is also a kind of reciprocal knowled
ge like TKK-construction (TKK from Tits-Kantor-Koecher): given a Jordan al
gebra one can assign to it a natural (but not functorial) Lie algebra. The
functoriality problem was solved by Alison and Gao\, we call it the TAG c
onstruction.\n\nWhen the natural representation $V$ also appears\, Elduque
et al. made the "translation" from Lie axioms into an object called "Jord
an triple".\n\nIf the algebra is a SUPER Lie algebra\, but VERY SHORT\, th
en both TKK and TAG constructions were generalized to the super case by Ba
rbier and Shang.\n\nIn this talk\, I will show that TKK and TAG constructi
ons can be extended to the SHORT super case. That is\, one can make a cons
truction beginning from a Jordan super triple (not just a Jordan algebra)
and get a Lie super algebra. In case the Jordan triple is a usual one\, we
get a reciprocal construction to Elduque's one. In case the Jordan triple
is just a Jordan algebra\, but super\, we generalize Shang's work for sup
er Jordan algebras. On the way of doing that\, adapting to the short case
an intrinsic description of Shang of the Jordan algebra associated to a ve
ry short Lie algebra\, we discover two different possible ternary Jordan s
tructure on the "Jordan data" associated to a short Lie algebra: one was c
onsidered previously by Elduque et al (in the non super case) and the othe
r can be described in a simpler way using the Lie-intrinsic description\,
and it happens that this second one is more suitable for the functorial ge
neralization of TKK and TAG construction for short (and super) constructio
n.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Safonkin (Leipzig University\, Germany)
DTSTART:20250609T150000Z
DTEND:20250609T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/126
DESCRIPTION:Title: What is a double star-product?\nby Nikita Safonkin (Leipzig Uni
versity\, Germany) as part of European Non-Associative Algebra Seminar\n\n
\nAbstract\nDouble Poisson brackets\, introduced by M. Van den Bergh in 20
04\, are noncommutative analogs of the usual Poisson brackets in the sense
of the Kontsevich-Rosenberg principle: they induce Poisson structures on
the space of N-dimensional representations of an associative algebra A fo
r any N. The problem of deformation quantization of double Poisson bracket
s was raised by D. Calaque in 2010\, and had remained open since then. In
the talk\, I plan to present a possible answer to the question in the titl
e. Namely\, I will discuss a structure on an associative algebra A that in
duces a star-product under the representation functor and\, therefore\, ac
cording to the Kontsevich-Rosenberg principle\, can be viewed as an analog
of star-products in noncommutative geometry. If time permits\, I will als
o discuss a way to invert the Kontsevich-Rosenberg principle by introducin
g the notion of a double algebra over an arbitrary operad. The talk is bas
ed on arXiv:2506.00699.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brais Ramos Pérez (University of Santiago de Compostela\, Spain)
DTSTART:20250616T150000Z
DTEND:20250616T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/127
DESCRIPTION:Title: Twisted relative Rota-Baxter operators and their relation with Hopf
trusses\nby Brais Ramos Pérez (University of Santiago de Compostela\
, Spain) as part of European Non-Associative Algebra Seminar\n\n\nAbstract
\nIn this talk we are going to introduce the category of twisted relative
Rota-Baxter operators in a braided monoidal setting together with a proced
ure for constructing examples of such structures based on idempotent Hopf
algebra morphisms\, and also we are going to prove that\, under certain co
nditions\, the following results hold: There exists an adjoint pair of fun
ctors between the category of Hopf trusses and the category of twisted rel
ative Rota-Baxter operators. The previous adjunction induces a categorical
equivalence between the category of Hopf trusses and the subcategory of i
nvertible twisted relative Rota-Baxter operators.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agata Pilitowska (Warsaw University of Technology\, Poland)
DTSTART:20250623T150000Z
DTEND:20250623T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/128
DESCRIPTION:Title: Diagonals of solutions of the Yang-Baxter equation\nby Agata Pi
litowska (Warsaw University of Technology\, Poland) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nThe Yang--Baxter equation is
one of the fundamental equations occurring in statistical mechanics and qu
antum field theory. I will show that the diagonal mappings are bijections
in any non-degenerate set-theoretical solution. This immediately gives tha
t any non-degenerate solution is bijective and affirmatively answers quest
ion stated by Cedo\, Jespers and Verwimp. I also prove that\, for a subcla
ss of solutions called permutational\, one-sided non-degeneracy is suffice
nt for the diagonal to be invertible. This is joint work with Premysl Jedl
icka (Czech University of Life Sciences).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Nardozza (University of Bari Aldo Moro\, Italy)
DTSTART:20250630T150000Z
DTEND:20250630T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/129
DESCRIPTION:Title: The Grassmann algebra: identities\, derivations\, and differential
identities\nby Vincenzo Nardozza (University of Bari Aldo Moro\, Italy
) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nStart
ing from Kemer's work\, the Grassmann algebra of an infinite-dimensional v
ector space played a key role in classical PI-Theory. Still\, there are ne
w branches of PI-Theory\, involving PI-algebras with additional structures
\, where the Grassmann algebra either is a key ingredient as well\, or lea
ds to interesting identities. In particular\, the differential identities
of the Grassmann algebra under some derivation action will be presented\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuan Pham (University of Edinburgh\, UK)
DTSTART:20250707T150000Z
DTEND:20250707T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/130
DESCRIPTION:Title: The orbit method for the Virasoro algebra\nby Tuan Pham (Univer
sity of Edinburgh\, UK) as part of European Non-Associative Algebra Semina
r\n\n\nAbstract\nThe orbit method is a fundamental tool to study a finite
dimensional solvable Lie algebra g. It relates the annihilators of irreduc
ible representation of \\g to the coadjoint orbits of g* . In my talk\, I
will extend this story to the Witt and Virasoro algebra infinite dimension
al Lie algebras which are important in physics and representation theory.
I will construct an induced module from an element of Vir* and show that i
ts annihilator is a primitive ideal. I will also construct an algebra homo
morphism that allows one to relate the orbit method for Vir to that of a f
inite dimensional solvable Lie algebra.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elkin Quintero Vanegas (Federal University of Amazonas\, Brazil)
DTSTART:20250714T150000Z
DTEND:20250714T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/131
DESCRIPTION:Title: Albert's Problem and its connections\nby Elkin Quintero Vanegas
(Federal University of Amazonas\, Brazil) as part of European Non-Associa
tive Algebra Seminar\n\n\nAbstract\nIn this talk\, we abord the question o
f existence of simple nilalgebras within the class of commutative power as
sociative algebras. We give some equivalences that related the existence
of such algebras to the non degenerated bilinear forms or faithful irreduc
ible modules.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastiano Argenti (University of Basilicata\, Italy)
DTSTART:20250721T150000Z
DTEND:20250721T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/132
DESCRIPTION:Title: Gradings on simple Lie superalgebras\nby Sebastiano Argenti (Un
iversity of Basilicata\, Italy) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nIn this talk\, we briefly discuss the recent deve
lopments regarding the classification of gradings on simple Lie superalgeb
ras. The interest on Lie superalgebras stems from theoretical physics whil
e the study of their algebraic properties was fostered by Kac and his clas
sification of the simple finite dimensional Lie superalgebras. The classif
ication of the gradings on such algebras is an ongoing work collecting the
efforts of many people. We will give an overview of the progress in this
direction and then we will focus on the case of exceptional simple Lie sup
eralgebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Sharma (Indian Institute of Technology Kanpur\, India)
DTSTART:20250818T150000Z
DTEND:20250818T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/133
DESCRIPTION:Title: Representation of map extended Witt algebras\nby Sachin Sharma
(Indian Institute of Technology Kanpur\, India) as part of European Non-As
sociative Algebra Seminar\n\n\nAbstract\nIn this talk\, I will speak on th
e classification result of irreducible modules for map extended Witt algeb
ras with finite-dimensional weight spaces. They turn out to be either modu
les with uniformly bounded weight spaces or highest-weight modules. We fur
ther prove that all these modules are single point evaluation modules (n
≥ 2). So they are actually irreducible modules for extended Witt algebra
s. This is a joint work with S. Eswara Rao\, Priyanshu Chakraborty\, and R
itesh Kumar Pandey.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Richter (Blekinge Institute of Technology\, Sweden)
DTSTART:20250825T150000Z
DTEND:20250825T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/134
DESCRIPTION:Title: Non-associative versions of Hilbert’s basis theorem\nby Johan
Richter (Blekinge Institute of Technology\, Sweden) as part of European N
on-Associative Algebra Seminar\n\n\nAbstract\nI will describe several non-
associative versions of Hilbert’s basis theorem\, for non-associative Or
e extensions and related structures. An interesting asymmetry between the
left and right versions of Hilbert’s basis theorem will appear\, not pre
sent in the associative case. The talk is based on joint work with Per Bä
ck.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Paniello (University of Zaragoza\, Spain)
DTSTART:20250901T150000Z
DTEND:20250901T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/135
DESCRIPTION:Title: Local inheritance in Jordan algebras of quotients\nby Irene Pan
iello (University of Zaragoza\, Spain) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nSince their introduction by K. Meyberg in
the nonassociative setting\, local algebras have played a key role in the
study of Jordan systems. The local inheritance of regularity conditions (
such as nondegenerancy\, strong primeness or primitivity) is a well-known
result that undoubtedly contributed to the development of the structure
theory\, not only of Jordan algebras\, but also of Jordan pairs and tripl
e systems. \n\nA rather usual strategy to tackle many Jordan questions
is to differentiate Jordan systems depending on whether their\n local a
lgebras satisfy or not certain properties. For instance\, some of the r
ecent results on localization theory for Jordan algebras have been establ
ished taking advantage of the \n dichotomy between Jordan algebras havin
g\, or not\, local algebras satisfying polynomial identities.\nAnalogous
ly\, the formulation of Goldie local theory for Jordan algebras is clo
sely related to Jordan algebras \nadmitting Lesieur-Croisot local algebr
as.\n \n \n The above considerations lead us to consider\, in the Jordan
algebra setting\, how local algebras of Jordan algebras interact with thei
r algebras of quotients (in Utumi's sense). This problem is motivated by
a previous question originally posed\, in the associative setting for (
maximal\, Martindale and symmetric) rings of quotients of semiprime rings
by G\\'omez Lozano and Siles Molina\, who proved that both constructions c
ommute whenever the element at which the local algebra is defined becomes
von Neumann regular in the corresponding ring of quotients. \n \n In thi
s talk we will display the Jordan algebra case of this problem\, proving t
hat\, for any nondegenerate Jordan algebra\, whenever the element defini
ng the local algebra becomes von Neumann regular in its maximal algebra
of quotients\, taking local algebras and maximal algebras of quotients a
re commuting constructions.\n \n \nThis is a joint work with Fernando Mont
aner (University of Zaragoza).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dijana Ilišević (University of Zagreb\, Croatia)
DTSTART:20251006T150000Z
DTEND:20251006T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/136
DESCRIPTION:Title: Spectral properties of isometries of JB*-triples and C*-algebras\nby Dijana Ilišević (University of Zagreb\, Croatia) as part of Europe
an Non-Associative Algebra Seminar\n\n\nAbstract\nA JB*-triple is a comple
x Banach space with a continuous non-associative triple product that satis
fies specific axioms. Any C*-algebra can be seen as a JB*-triple with resp
ect to the triple product defined using the algebra product and the involu
tion. Surjective linear isometries of JB*-triples are closely related to t
he corresponding algebraic isomorphisms. The aim of this talk is to recall
and connect some recent and not so recent results on the structure of sur
jective isometries of JB*-triples\, specifically C*-algebras\, following a
long line of work starting with the celebrated Banach-Stone theorem. Atte
ntion will be focused on periodic isometries\, their eigenprojections and
eigenvalues. They will be studied in connection with the following inverse
eigenvalue problem for isometries: when is a given finite set of modulus
one complex numbers spectrum of a surjective linear isometry? The necessar
y conditions on such a set will be presented.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Blumer (University of Vienna\, Austria)
DTSTART:20250526T150000Z
DTEND:20250526T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/137
DESCRIPTION:Title: Quadratically defined Lie algebras and HNN-extension\nby Simone
Blumer (University of Vienna\, Austria) as part of European Non-Associati
ve Algebra Seminar\n\n\nAbstract\nIn this talk\, we will delve into the cl
ass of Lie algebras defined by quadratic relations\, focusing on the expli
cit computation of their cohomology rings in specific cases. These algebra
s naturally arise in the broader context of positively graded Lie algebras
\, where they play a significant structural role. The theory of HNN-extens
ions plays a crucial role in this context\, providing a powerful tool for
decomposing quadratic Lie algebras into smaller components. Moreover\, we
will explore how HNN-extensions can be used to embed finitely presented po
sitively graded Lie algebras into quadratic ones.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zohreh Ravanpak (West University of Timisoara\, Romania)
DTSTART:20250728T150000Z
DTEND:20250728T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/138
DESCRIPTION:Title: NL Bialgebras: Structures\, Hierarchies\, and Applications in Integ
rable Systems\nby Zohreh Ravanpak (West University of Timisoara\, Roma
nia) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn
this talk\, I will introduce the concept of NL bialgebras\, an algebraic
structure that combines a Lie bialgebra with a Nijenhuis operator on a Lie
algebra. The compatibility between these two structures leads to a rich f
ramework for studying deformations and hierarchies of Lie bialgebras. As a
n important application\, I will show how the underlying algebraic framewo
rk of the Euler-top system can be represented as a weak NL bialgebra\, hig
hlighting the significance of these structures in the context of integrabl
e systems.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Guimarães (Federal University of Rio Grande do Norte\, Brazi
l)
DTSTART:20250804T150000Z
DTEND:20250804T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/139
DESCRIPTION:Title: A characterization of the natural grading of the Grassmann algebra<
/a>\nby Alan Guimarães (Federal University of Rio Grande do Norte\, Brazi
l) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nLet
E be the infinite-dimensional Grassmann algebra over a field of characteri
stic different from 2. In this talk\, we investigate the Isomorphism Probl
em in the context of the natural Z2-grading of E. We show that this gradin
g is completely determined by its graded polynomial identities. Additional
ly\, we explore the connection between Z2-gradings on E and its automorphi
sms of order two.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Saracco (University of Seville\, Spain)
DTSTART:20250915T150000Z
DTEND:20250915T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/140
DESCRIPTION:Title: Integrals for bialgebras\nby Paolo Saracco (University of Sevil
le\, Spain) as part of European Non-Associative Algebra Seminar\n\n\nAbstr
act\nAn extremely familiar notion in Hopf algebra theory is that of an \\e
mph{integral}. If $G$ is a compact topological group\, then a Haar integra
l on $G$ is a linear functional $\\mathcal{C}(G) \\to \\mathbb{R}$ which i
s translation invariant.\n%\nA well-known result by Larson and Sweedler sh
ows that integrals on a Hopf algebra can be obtained by applying the Struc
ture Theorem of Hopf modules to the rational part of its linear dual\, i.e
.\, the space of integrals comes from a right adjoint functor from a categ
ory of modules to the category of vector spaces. \n%\nIn this seminar we w
ill discuss how this construction can be carried out even in the absence o
f an antipode\, offering a novel perspective on integrals which differs pr
ofoundly from their classical description as ``colinear forms''. Our appro
ach leads to a new notion of integrals for bialgebras which does not requi
re\, and does not imply\, the existence of an antipode.\n\nTime permitting
\, we will seize this opportunity to say a few words about Hopf envelopes
of bialgebras\, since in many cases of interest integrals for a bialgebra
are in bijection with integrals for its Hopf envelope.\n%\nThe Hopf envelo
pe of a bialgebra B is a certain universal Hopf algebra that we can associ
ate with B and that plays for it the same role that the universal envelopi
ng group plays for a monoid. \n%In categorical terms\, the Hopf envelope i
s the left adjoint to the forgetful functor from Hopf algebras to bialgebr
as\, hence it may be legitimately called the free Hopf algebra generated b
y B. \nIts existence is a well-known fact in Hopf algebra theory\, but its
construction is very technical. Nevertheless\, there are a number of case
s where we can realize the Hopf envelope of a bialgebra B as a suitable qu
otient of B itself and we can take advantage of it to study integrals for
the corresponding bialgebra.\n\n\\medskip\n\n\\centering \nThis talk is ba
sed on an ongoing project with A.\\ Ardizzoni and C.\\ Menini.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Marrani (University of Hertfordshire\, UK)
DTSTART:20250922T150000Z
DTEND:20250922T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/141
DESCRIPTION:Title: Okubo Algebra: a new approach to Quantum Chromodynamics?\nby Al
essio Marrani (University of Hertfordshire\, UK) as part of European Non-A
ssociative Algebra Seminar\n\n\nAbstract\nThis talk discusses the possible
relevance of the Okubonions (i.e. the real Okubo algebra) in quantum chro
modynamics (QCD). We start and present the Okubonions within the 8-dimensi
onal real division composition algebras\, and then discuss their realizati
on as the traceless cubic simple Jordan algebra over the complex numbers\,
endowed with a suitable deformation of the Michel-Radicati product. The O
kubonions lack a unit element and exhibit the unique feature of sitting in
the adjoint representation of their automorphism group SU(3)\; in this re
spect\, they are fundamentally different from the better-known Octonions.
While these latter may represent quarks (and singlets of the QCD SU(3) col
or gauge group)\, the Okubonions are conjectured to represent the gluons\,
i.e. the gauge bosons of the colour group. However\, it is remarked that
the SU(3) groups pertaining to Okubonions and Octonions are distinct and i
nequivalent subgroups of Spin(8) that share no common SU(2) subgroup. Main
reference : arXiv:2309.17435 [hep-th]\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abror Khudoyberdiyev (Institute of Mathematics\, Uzbekistan)
DTSTART:20250811T150000Z
DTEND:20250811T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/142
DESCRIPTION:Title: Transposed Poisson structures and quasi-derivations\nby Abror K
hudoyberdiyev (Institute of Mathematics\, Uzbekistan) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk\, we describe
transposed Poisson structures on Witt and Virasoro-type algebras. We compu
te 1/2-derivations on the deformative Schrodinger-Witt algebra\, not-finit
ely graded Witt algebras\, and not-finitely graded Heisenberg-Witt algebra
s. We classify all transposed Poisson structures on such algebras\, as wel
l as deformed generalized Heisenberg-Virasoro and not-finitely graded Heis
enberg-Virasoro algebras. Furthermore\, we compute the quasi-derivations o
f the Witt and Virasoro algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nishant Rathee (IISER Mohali\, India)
DTSTART:20250929T150000Z
DTEND:20250929T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/143
DESCRIPTION:Title: Extensions of Skew Braces\nby Nishant Rathee (IISER Mohali\, In
dia) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nSk
ew braces are important algebraic structures arising from non-degenerate s
et-theoretic solutions of the Yang–Baxter equation. In this talk\, we di
scuss extensions of skew braces and their connection with the second cohom
ology group. We will also see how an action of a skew brace on an abelian
group naturally induces a representation of the skew brace. Furthermore\,
we explore split extensions of skew braces and their relation to the split
ting of group extensions.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilja Gogić (University of Zagreb\, Croatia)
DTSTART:20251013T150000Z
DTEND:20251013T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/144
DESCRIPTION:Title: Spectrum-shrinking maps and nonlinear preservers on matrix domains<
/a>\nby Ilja Gogić (University of Zagreb\, Croatia) as part of European N
on-Associative Algebra Seminar\n\n\nAbstract\nThe celebrated Kaplansky–A
upetit conjecture asks whether\nevery surjective linear map between unital
semisimple Banach algebras\nthat shrinks the spectrum must be a Jordan ho
momorphism. While the\nconjecture has been resolved in specific settings (
most notably for\nvon Neumann algebras by Aupetit and for algebras of boun
ded linear\noperators on Banach spaces by Sourour)\, it remains widely ope
n\, even\nfor C*-algebras. In contrast\, spectrum-preserving maps are ofte
n more\naccessible\, and a natural question is whether results in that set
ting\ncan be extended to the spectrum-shrinking case. However\, existing\n
results indicate that such generalizations are typically far more\ndelicat
e. Motivated by this\, the talk investigates continuous\nspectrum-shrinkin
g maps from various subsets Xₙ of the complex matrix\nalgebra Mₙ with
values in another matrix algebra Mₘ. The classes of\ndomains Xₙ under
consideration include structural matrix algebras\n(i.e. subalgebras of M
ₙ containing all diagonal matrices)\, the sets of\nnormal and singular m
atrices\, and matrix Lie groups such as GL(n)\,\nSL(n)\, and U(n). Our fir
st objective is to determine when such\nspectrum-shrinking maps automatica
lly preserve the spectrum. Building\non this\, and Šemrl’s influential
nonlinear characterization of Jordan\nautomorphisms of Mₙ (when n ≥ 3)
as continuous maps preserving both\nspectrum and commutativity\, our seco
nd objective is to establish an\nanalogous nonlinear preserver theorem for
maps Xₙ → Mₙ. This is based\non joint work with Alexandru Chirvasit
u (University at Buffalo) and\nMateo Tomašević (University of Zagreb).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Roca i Lucio (Paris Cité University\, France)
DTSTART:20251020T150000Z
DTEND:20251020T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/145
DESCRIPTION:Title: Higher Lie theory in positive characteristic\nby Victor Roca i
Lucio (Paris Cité University\, France) as part of European Non-Associativ
e Algebra Seminar\n\n\nAbstract\nGiven a nilpotent Lie algebra over a char
acteristic zero field\, one can construct a group in a universal way via t
he Baker-Campbell-Hausdorff formula. This integration procedure admits gen
eralizations to dg Lie or L-infinity-algebras\, giving in general infinity
-groupoid of deformations that it encodes\, as by the Lurie-Pridham corres
pondence\, infinitesimal deformation problems are equivalent to dg Lie alg
ebras. The recent work of Brantner-Mathew establishes a correspondence bet
ween infinitesimal deformation problems and partition Lie algebras over a
positive characteristic field. In this talk\, I will explain how to constr
uct an analogue of the integration functor for certain point-set models of
(spectral) partition Lie algebras\, and how this integration functor can
recover the associated deformation problem under some assumptions. Further
more\, I will discuss some applications of these constructions to unstable
p-adic homotopy theory.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michiel Smet (Ghent University\, Belgium)
DTSTART:20251027T150000Z
DTEND:20251027T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/146
DESCRIPTION:Title: Cubic norm pairs and hermitian cubic norm structures\nby Michie
l Smet (Ghent University\, Belgium) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nCubic norm structures were originally introdu
ced by McCrimmon to generalize Springer's construction of Jordan algebras
from a pairing of cubic forms. These cubic norm structures appear naturall
y in the study of (exceptional) Lie algebras and (exceptional) linear alge
braic groups. Later\, Allison introduced structurable algebras. One of the
main classes of structurable algebras is closely related to cubic norm st
ructures. Moreover\, the natural appearances of cubic norm structures can
often be understood in terms of this class of structurable algebras. To be
tter understand this class of structurable algebras\, De Medts introduced
hermitian cubic norm structures.\nIn this talk\, we introduce cubic norm p
airs and hermitian cubic norm structures over arbitrary commutative rings
and construct an associated structurable algebra\, Lie algebra\, and autom
orphism group. We also study the behaviour of certain automorphism groups.
\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaomin Tang (Heilongjiang University\, China)
DTSTART:20251103T150000Z
DTEND:20251103T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/147
DESCRIPTION:Title: Toroidal Cluster Algebra and the Toroidal Grothendieck ring of a te
nsor category\nby Xiaomin Tang (Heilongjiang University\, China) as pa
rt of European Non-Associative Algebra Seminar\n\n\nAbstract\nLet U be the
quantum loop algebra corresponding to a simple Lie algebra and K be the
Grothendieck ring of a specific tensor category consisting of finite-dime
nsional U-modules\, which possesses a natural cluster algebra structure.
In this talk\, we delineate a toroidal cluster structure endowed with two
parameters on the toroidal Grothendieck ring K of the monomial category C
\, which is intimately tied to the quantum loop algebra of type A3.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ginevra Giordani (University of L'Aquila\, Italy)
DTSTART:20251110T150000Z
DTEND:20251110T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/148
DESCRIPTION:Title: Central exponent in PI-theory\nby Ginevra Giordani (University
of L'Aquila\, Italy) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nThe algebras that satisfy at least a non-trivial polynomial
identity are called PI-algebras. They can be seen as a generalization of
the commutative world and PI-theory is the research field in modern algebr
a studying the identities satisfied by these algebras. In its general case
this is a very difficult problem\, so that a combinatoric approach is gen
erally used. \n\nWe will briefly introduce polynomial identities and PI-al
gebras\, giving also some motivations\, and we will present the main resul
ts in PI-theory.\n\nThen\, we will introduce central polynomials\, explain
ing why they are important for the research on polynomial indentities.\nTh
eir behavior can be also studied by analyzing the behavior of the dimensio
n $c_n^z(A)$ of the space of multilinear polynomials of degree $n$ modulo
the central polynomials of an associative PI-algebra $A$. In 2018\, Giambr
uno and Zaicev established\, for associative algebras\, the existence of t
he limit\n$$\n\\lim_{n \\to \\infty} \\sqrt[n]{c_n^z(A)}.\n$$\nIn this tal
k we present research advances on this problem\, with special focus on ass
ociative superalgebras with superinvolution.\n\nThis talk is based on a jo
int work with Antonio Ioppolo\, Antônio Augusto dos\nSantos and Ana Crist
ina Vieira.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iván Ruiz Campos (University of Málaga\, Spain)
DTSTART:20250908T150000Z
DTEND:20250908T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/149
DESCRIPTION:Title: The affine group scheme of the automorphisms of evolution algebras
of dimension 2.\nby Iván Ruiz Campos (University of Málaga\, Spain)
as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this
talk we establish a connection between evolution algebras of dimension tw
o and Hopf algebras\, via the algebraic group of automorphisms of an evolu
tion algebra. This analysis involves the computation of the (tight) p−al
gebra associated with any 2-dimensional evolution algebra\, whenever it ex
ists. Furthermore\, if A is perfect and has a faithful tight p-algebra\, t
hen this p-algebra is isomorphic to H (the Hopf algebra associated to the
evolution algebra).\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Zaitseva (HSE University\, Russia)
DTSTART:20251117T150000Z
DTEND:20251117T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/150
DESCRIPTION:Title: Derivations on toric and trinomial algebras\nby Yulia Zaitseva
(HSE University\, Russia) as part of European Non-Associative Algebra Semi
nar\n\n\nAbstract\nA derivation D on an algebra A is said to be locally ni
lpotent if any element of A is annihilated by some power of D. If A is an
algebra of regular functions on an affine algebraic variety X\, then local
ly nilpotent derivations on A correspond to actions of one-parameter unipo
tent subgroups on X. In turn\, actions of tori on X correspond to gradings
on A. I will survey some classification results about homogeneous locally
nilpotent derivations on toric varieties and their generalizations.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerardo Martín Escolano (University of Granada\, Spain)
DTSTART:20251124T150000Z
DTEND:20251124T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/151
DESCRIPTION:Title: Preserver Problems on Jordan Banach algebras and applications\n
by Gerardo Martín Escolano (University of Granada\, Spain) as part of Eur
opean Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk we will
discuss about many topics related with preserver problems in Jordan Banach
algebras\, in particular\, we will talk about the Lie-Trotter formula for
Jordan Banach algebras and its application in the study of spectral-value
d multiplicative functionals. Moreover we will present some results relate
d with maps preserving what is called strong commutativity or operator com
mutativity. Finally\, we will discuss about the Mackey-Gleason problem for
Jordan Banach algebras and if time permits\, we will show how this result
can be applied in the study of piecewise Jordan homomorphism.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vicent Pérez Calabuig (University of Valencia\, Spain)
DTSTART:20251201T150000Z
DTEND:20251201T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/152
DESCRIPTION:Title: On left nilpotent skew braces of class 2\nby Vicent Pérez Cala
buig (University of Valencia\, Spain) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nIn this seminar\, a detailed study of left
nilpotent skew braces B of class 2 will be carried out. We shall see that
in the case that B is of nilpotent type\, then it is centrally nilpotent\;
in particular\, if B is of abelian type then it is right nilpotent of cla
ss 3. This opens the door to know much more about the inner structure of l
eft nilpotent skew braces of class 2 and its associated solution of the Ya
ng-Baxter equation. In the abelian type case\, we shall delve into the des
cription of these finitely generated braces.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azamat Saydaliyev (Institute of Mathematics\, Uzbekistan)
DTSTART:20251208T150000Z
DTEND:20251208T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/153
DESCRIPTION:Title: Algebraic and geometric classification of non-associative algebras<
/a>\nby Azamat Saydaliyev (Institute of Mathematics\, Uzbekistan) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk\,
we study the algebraic and geometric classification of several families of
non-associative algebras\, including Jordan superalgebras\, F-manifold al
gebras\, $\\delta$-Poisson algebras\, and transposed $\\delta$-Poisson alg
ebras. After briefly recalling the definitions and known results\, we comp
are their algebraic and geometric classification. We conclude by presentin
g new classification results obtained in our work.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Draper Fontanals (University of Málaga\, Spain)
DTSTART:20251215T150000Z
DTEND:20251215T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/154
DESCRIPTION:Title: Revisiting simple Lie algebras from the view of the grading group\nby Cristina Draper Fontanals (University of Málaga\, Spain) as part o
f European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk we
discuss the role of gradings on Lie algebras and how they can be used to o
btain suitable models for a wide range of structures\, including simple\,
solvable\, and nilpotent Lie algebras. We introduce the notion of a \\emph
{generalized group algebra}\, which provides a flexible framework for desc
ribing graded algebras in full generality. Although this concept may at fi
rst appear too broad to be useful in the specific context of Lie algebras\
, we shall show how naturally it applies by examining several illustrative
examples.\n\nA central theme will be the use of the \\emph{grading group}
to gain insight into structural properties of the underlying Lie algebra.
For instance\, viewing $\\mathfrak{so}(8)$ as a generalized group algebra
sheds light on its spin representations and on the phenomenon of triality
. More broadly\, this perspective greatly simplifies the construction of o
rthonormal bases\, as in the case of $\\mathfrak{g}_2$.\n\nFinally\, we sh
ow that this approach renders the computation of brackets in Lie algebras
obtained via \\emph{graded contractions} essentially immediate. This leads
to vast families of high-dimensional nonsimple Lie algebras with distinct
ive structural features\, obtained from the exceptional simple Lie algebra
s through the Tits construction.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateo Tomašević (University of Zagreb\, Croatia)
DTSTART:20260105T150000Z
DTEND:20260105T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/155
DESCRIPTION:Title: Automatic additivity of multiplicative and Jordan multiplicative ma
ps\nby Mateo Tomašević (University of Zagreb\, Croatia) as part of E
uropean Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk\, we d
iscuss the problem of automatic additivity for multiplicative maps between
rings\, following the classical results of Martindale and Jodeit-Lam. We
present a complete description of Jordan multiplicative self-maps on full
matrix algebras M_n(F)\, where F is a field of characteristic not equal to
2. Without imposing additional assumptions\, we show that such maps are e
ither constant (and equal to a fixed idempotent)\, or additive (and hence
Jordan monomorphisms). This result is joint work with Ilja Gogić.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramón González Rodríguez (University of Vigo\, Spain)
DTSTART:20260112T150000Z
DTEND:20260112T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/156
DESCRIPTION:Title: Quasigroupoids and weak Hopf quasigroups\nby Ramón González R
odríguez (University of Vigo\, Spain) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nQuasigroupoids and weak Hopf quasigroups a
re non associative generalizations of groupoids and weak Hopf algebras. In
this talk we will show that the category of finite quasigroupoids is equ
ivalent to the one of pointed cosemisimple weak Hopf quasigroups over a gi
ven field K. As a consequence\, we obtain a categorical equivalence betwe
en the categories of quasigroups\, in the sense of Klim and Majid (i.e.\,
loops with the inverse property)\, and the category of pointed cosemisimpl
e Hopf quasigroups over K. On the other hand\, in this talk we introduce
the notion of exact factorization of a quasigroupoid and the notion of ma
tched pair of quasigroupoids with common base. We prove that if (A\,H) is
a matched pair of quasigroupoids it is posible to construct a new quasigro
upoid called the double cross product of A and H. Moreover\, we show tha
t\, if a quasigroupoid B admits an exact factorization\, there exists a m
atched pair of quasigroupoids (A\,H) and an isomorphism of quasigroupoid
s between the double cross product of A and H and B. Finally\, we show t
hat every matched pair of quasigroupoids (A\,H) induces\, thanks to the qu
asigroupoid magma construction\, a pair (K[A]\, K[H]) of weak Hopf quasigr
oups and a double crossed product of weak Hopf quasigroups isomorphic as w
eak Hopf quasigroups to the quasigroupoid magma of the double cross produ
ct gorupoid of A and H .\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Grantcharov (University of Texas at Arlington\, USA)
DTSTART:20260119T150000Z
DTEND:20260119T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/157
DESCRIPTION:Title: U(h)-Free sl(2)-Modules of rank 2\nby Dimitar Grantcharov (Univ
ersity of Texas at Arlington\, USA) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nIn this talk\, we will discuss non-weight mod
ules over the Lie algebra sl(2). More precisely\, we focus on modules that
are free of finite rank over the universal enveloping algebra U(h) of a C
artan subalgebra h of sl(2). In particular\, we will present a new family
of simple U(h)-free modules of rank 2. The talk is based on joint work wit
h K. Nguyen and K. Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernardo Leite da Cunha (University of Santiago de Compostela\, Sp
ain)
DTSTART:20260126T150000Z
DTEND:20260126T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/158
DESCRIPTION:Title: Representations of two-dimensional compatible Lie algebras\nby
Bernardo Leite da Cunha (University of Santiago de Compostela\, Spain) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nA compatib
le Lie algebra is a vector space equipped with two Lie products such that
any linear combination of them is also a Lie product. These algebras arose
from the related class of compatible Poisson algebras in the context of m
athematical physics and Hamiltonian mechanics.\nIn this talk\, we start by
stating some basic definitions and results about compatible Lie algebras.
We then present counterexamples to analogues of some of the most importan
t theorems in Lie algebra theory\, namely the theorems of Weyl and Levi\,
highlighting how compatible Lie algebras can behave very differently from
Lie algebras.\nWe then move on to studying the representation theory of a
family of simple two-dimensional compatible Lie algebras. We construct a f
amily of irreducible representations for each algebra of this family\, and
thereafter\, we focus on one specific simple two-dimensional compatible L
ie algebra in order to make the computations simpler and results easier to
state and prove. In this setting\, we prove a Clebsch-Gordan formula for
the irreducible representations previously described\, and we also exhibit
a second family of representations\, this time "breaking" Weyl's theorem
(i.e.\, reducible and indecomposable representations over the field of com
plex numbers).\nTime permitting\, we finish by discussing the failure of f
urther central results from Lie algebra theory in this broader context\, i
ncluding the characterization of semisimple algebras and the Whitehead Lem
mas.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zahra Nazemian (University of Graz\, Austria)
DTSTART:20260202T150000Z
DTEND:20260202T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/159
DESCRIPTION:Title: Aut-stable subspaces of algebras and beyond\nby Zahra Nazemian
(University of Graz\, Austria) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nIn this talk\, we recall some challenging problems
in algebra\, such as the characterization problem of polynomial rings\, t
he automorphism groups of certain algebras\, and the Dixmier property of a
lgebras. We then explain how the concept of Aut-stable subspaces can be us
ed as a tool to approach these problems.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Cuypers (Eindhoven University of Technology\, Netherlands)
DTSTART:20260209T150000Z
DTEND:20260209T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/160
DESCRIPTION:Title: Every group is automorphism group of a simple algebra\nby Hans
Cuypers (Eindhoven University of Technology\, Netherlands) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nPopov raised the ques
tion whether each finite group is the automorphism group of a finite dimen
sional simple algebra. He and Gordeev provided an affirmative answer for
sufficiently large enough fields\, not only for finite groups\, but also f
or algebraic groups. We will show that for each field F and each (finite)
group G there are infinitely many (finite) dimensional simple algebras
with G as automorphism group. If F has at least 4 elements the algebras
can be commutative as well as non-commutative.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Ferri (University of Torino\, Italy)
DTSTART:20260216T150000Z
DTEND:20260216T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/161
DESCRIPTION:Title: From sets to quivers: oidification and the Yang-Baxter equation
\nby Davide Ferri (University of Torino\, Italy) as part of European Non-A
ssociative Algebra Seminar\n\n\nAbstract\nThe Yang-Baxter equation\, or br
aid relation\, can be defined in any monoidal category. In the category Se
t\, much is known about its solutions. In this seminar I describe the mono
idal category Quiv_\\Lambda of quivers over a fixed set of vertices \\Lamb
da. I introduce the philosophy called "oidification"\, which turns sets in
to quivers\, groups into groupoids\, algebras into algebroids\, etc. Final
ly\, I give an overview of the theory of the Yang-Baxter equation in Quiv_
\\Lambda\, why it is relevant\, what still works as in Set (and what works
better than in Set!)\, and how it relates to the theory of partial soluti
ons and partial algebraic structures.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saikat Goswami (Institute for Advancing Intelligence\, India)
DTSTART:20260223T150000Z
DTEND:20260223T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/162
DESCRIPTION:Title: Universal Constructions on Algebras over Operads\nby Saikat Gos
wami (Institute for Advancing Intelligence\, India) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nWe construct a universal coac
ting bialgebra and Hopf algebra for any finite-dimensional algebra over a
symmetric operad. This work extends previous constructions of Agore and Mi
litaru to the operadic setting. We show that the category of finite-dimens
ional algebras over operads is enriched over the dual of commutative algeb
ras\, which induces a canonical bialgebra structure on the associated univ
ersal coacting algebra. Our framework recovers known constructions for Lie
\, Leibniz\, and Poisson algebras\, offering a unified operadic perspectiv
e on coacting objects across a broad class of algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Chapman (Academic College of Tel-Aviv-Yaffo\, Israel)
DTSTART:20260302T150000Z
DTEND:20260302T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/163
DESCRIPTION:Title: Measuring the associativity of loops\nby Adam Chapman (Academic
College of Tel-Aviv-Yaffo\, Israel) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nIn group theory folklore\, there is a well-k
nown theorem\; The probability that two randomly uniformly chosen elements
commute in a non-abelian group $G$ cannot exceed 5/8. The bound is attain
ed by the Quaternion group $Q_8$. In this talk\, we shall discuss a non-as
sociative analog of the theorem. Namely\, the probability of three randoml
y chosen elements associating is bounded by 43/64 in Moufang loops with nu
clear commutators\, with the bound attained by the Octonion loop $O_{16}$.
\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucia Bagnoli (Sapienza University of Rome\, Italy)
DTSTART:20260309T150000Z
DTEND:20260309T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/164
DESCRIPTION:Title: On new classes of quantum vertex algebras\nby Lucia Bagnoli (Sa
pienza University of Rome\, Italy) as part of European Non-Associative Alg
ebra Seminar\n\n\nAbstract\nWe present the construction of a new class of
quantum vertex algebras associated with a normalized Yang R-matrix. They a
re obtained as Yangian deformations of certain S-commutative quantum verte
x algebras and their S-locality takes the form of a single RTT relation. W
e establish some preliminary results on their representation theory and th
en further investigate their braiding map. These results were obtained joi
ntly with Slaven Kožić. Then we will discuss a recent generalization of
these results to the case of the type A trigonometric R-matrix. These resu
lts were obtained jointly with Marijana Butorac and Slaven Kožić.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Dietzel (University of Caen Normandy\, France)
DTSTART:20260316T150000Z
DTEND:20260316T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/165
DESCRIPTION:Title: A Brief Guide to Cabling and Endocabling.\nby Carsten Dietzel (
University of Caen Normandy\, France) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nCabling is a method developed by Lebed\, Ra
mìrez and Vendramin to deform involutive\, non-degenerate solutions to th
e Yang-Baxter equations while keeping control over the diagonal maps of th
e resulting solutions. This powerful tool allows one to prove a plethora o
f decomposability results for involutive solutions and has recently been g
eneralized by Colazzo and Van Antwerpen to obtain similar results for non-
involutive solutions. In this talk\, I will give an outline of classical c
abling in the style of Lebed\, Ramìrez and Vendramin\, and explain some s
tandard applications of the method. Afterwards\, I will demonstrate how cl
assical cabling can be generalized to endocabling\, where involutive solut
ions are deformed by means of endomorphisms of the module structure of per
mutation braces which is given by the λ-action. Finally\, I will give a r
ough sketch how endocabling can be applied to provide insights into the st
ructure of solutions whose diagonal map is a cyclic permutation.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:István Heckenberger (Philipps University Marburg\, Germany)
DTSTART:20261012T150000Z
DTEND:20261012T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/166
DESCRIPTION:Title: Pointed Hopf algebras of odd dimension\nby István Heckenberger
(Philipps University Marburg\, Germany) as part of European Non-Associati
ve Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/78
03181064\n\nAbstract\nIn joint work with Andruskiewitsch and Vendramin we
proved that over algebraically closed fields of characteristic zero\, poin
ted Hopf algebras of odd dimension are cocycle deformations of bosonizatio
ns of Nichols algebras of diagonal type. The proof is based on deep result
s of several people about pointed Hopf algebras with abelian coradical\, a
nd on a new deformation argument for solvable groups. I will explain the n
otions in the theorem and give some details about the proof.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/166/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willian Franca (Federal University of Juiz de Fora\, Brazil)
DTSTART:20260330T150000Z
DTEND:20260330T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/167
DESCRIPTION:Title: Applications of compact multipliers to algebrability of $(\\ell_{\\
infty}\\setminus c_0)\\cup\\{0\\}$ and $(B(\\ell_2(\\mathbb{N}))\\setminus
K(\\ell_2(\\mathbb{N}))\\cup \\{ 0\\}.$\nby Willian Franca (Federal U
niversity of Juiz de Fora\, Brazil) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nIn present talk we deal with the class $\\mat
hcal{C}=\\mathcal{C}_1\\cup \\mathcal{C}_2$ where $\\mathcal{C}_1$ (res
pectively\, $\\mathcal{C}_2$) is formed by all separable Uniform algebras
(respectively\, separable commutative C$^*$-algebras) with no compact e
lements. For a given algebra $A$ in $\\mathcal{C}_1$ (respectively\, $A$
in $\\mathcal{C}_2$) we will show that $A$ is isometrically isomorphic a
s algebra (respectively\, as C$^*$-algebra) to a subalgebra $M$ of $\\ell_
{\\infty}$ with $M\\subset (\\ell_{\\infty}\\setminus c_0)\\cup\\{0\\}.$ U
nder the additional assumption that $A$ is non-unital we verify that ther
e exists a copy of $M(A)$ (the multipliers algebra of $A$ which is non-sep
arable) inside $(\\ell_{\\infty}\\setminus c_0)\\cup\\{0\\}$.\n\nFor an in
finitely generated abelian C$^*$-algebra $B\,$ we will study the least car
dinality possible of a system of generators ($\\gn_{C^*}(B)$). In fact we
will deduce that $\\gn_{C^*}(B)$ coincides with the smallest cardinal numb
er $n$ such that an embedding of $\\Delta(B)$ (= the spectrum of $B$) i
n $\\mathbb{R}^n$ exists - The finitely generated version of this result w
as proved by Nagisa.\nIn addition\, we will introduce new concepts of alg
ebrability in terms of $\\gn_{C^*}(B)$ ($(C^*)$-genalgebrability) and its
natural variations.\n\nFrom our methods we will infer that there is $^*$-
isomorphic copy of $\\ell_{\\infty}$ in $(\\ell_{\\infty}\\setminus c_0)\\
cup\\{0\\}$. In particular\, $(\\ell_{\\infty}\\setminus c_0)\\cup\\{0\\}$
contains a copy of every separable Banach space.\nMoreover\, all the pos
itive answers of this work holds if we replace the set $(\\ell_{\\infty}\\
setminus c_0)\\cup\\{0\\}$ with $(B(\\ell_2(\\mathbb{N}))\\setminus K(\\el
l_2(\\mathbb{N}))\\cup \\{ 0\\}.$\n\nThis is a joint work with Jorge J. Ga
rcés (Universidad Politécnica de Madrid)\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rong Tang (Jilin University\, China)
DTSTART:20260406T150000Z
DTEND:20260406T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/168
DESCRIPTION:Title: Homotopy theory of post-Lie algebras\nby Rong Tang (Jilin Unive
rsity\, China) as part of European Non-Associative Algebra Seminar\n\n\nAb
stract\nGuided by Koszul duality theory\, we consider the graded Lie algeb
ra of coderivations of the cofree conilpotent graded cocommutative cotrial
gebra generated by $V$. We show that in the case of $V$ being a shift of a
n ungraded vector space $W$\, Maurer-Cartan elements of this graded Lie al
gebra are exactly post-Lie algebra structures on $W$. The cohomology of a
post-Lie algebra is then defined using Maurer-Cartan twisting. The secon
d cohomology group of a post-Lie algebra has a familiar interpretation as
equivalence classes of infinitesimal deformations. Next we define a post-L
ie$_\\infty$ algebra structure on a graded vector space to be a Maurer-Ca
rtan element of the aforementioned graded Lie algebra. Post-Lie$_\\infty$
algebras admit a useful characterization in terms of $L_\\infty$-actions (
or open-closed homotopy Lie algebras). Finally\, we introduce the notion o
f homotopy Rota-Baxter operators on open-closed homotopy Lie algebras and
show that certain homotopy Rota-Baxter operators induce post-Lie$_\\infty$
algebras. This is a joint work with Andrey Lazarev and Yunhe Sheng.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ferrara (Pegaso University\, Italy)
DTSTART:20260413T150000Z
DTEND:20260413T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/169
DESCRIPTION:Title: A Sylow Theorem for Some Classes of Finite Skew Braces\nby Mari
a Ferrara (Pegaso University\, Italy) as part of European Non-Associative
Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/78031
81064\n\nAbstract\nWe study a skew brace analogue of the First Sylow Theor
em for finite groups. Although a general version of this result is not yet
available in the context of skew braces\, we show that it holds for sever
al notable classes of finite skew braces\, including the supersolvable one
s. This work is carried out in collabora- tion with Andrea Caranti\, Ilari
a Del Corso\, Massimiliano Di Matteo\, and Marco Trombetti.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/169/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lau (Laval University\, Canada)
DTSTART:20260420T150000Z
DTEND:20260420T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/170
DESCRIPTION:Title: Lie algebra representations and free Jordan algebras\nby Michae
l Lau (Laval University\, Canada) as part of European Non-Associative Alge
bra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/780318106
4\n\nAbstract\nFor any unital Jordan algebra\, the famous Tits-Kantor-Koec
her construction produces an sl(2)-graded Lie algebra. We will look at we
ight modules for universal central extensions of these algebras\, concentr
ating on categories of modules satisfying combinatorial dominance or smoot
hness conditions. We describe some finiteness results for algebras and We
yl modules in these contexts. Surprisingly\, the proofs of several of our
results use Zelmanov's theorem on nil Jordan algebras of bounded index.
This talk is based on joint work with Olivier Mathieu.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/170/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdenacer Makhlouf (University of Haute Alsace\, France)
DTSTART:20260427T150000Z
DTEND:20260427T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/171
DESCRIPTION:by Abdenacer Makhlouf (University of Haute Alsace\, France) as
part of European Non-Associative Algebra Seminar\n\nInteractive livestrea
m: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/171/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Per Bäck (Mälardalen University\, Sweden)
DTSTART:20260504T150000Z
DTEND:20260504T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/172
DESCRIPTION:Title: Hilbert’s Basis Theorem for Noncommutative\, Nonassociative Polyn
omial Rings\nby Per Bäck (Mälardalen University\, Sweden) as part of
European Non-Associative Algebra Seminar\n\nInteractive livestream: https
://us02web.zoom.us/j/7803181064\n\nAbstract\nIn this talk\, I will introdu
ce Ore extensions\, the principal noncommutative generalization of polynom
ial rings\, and recall how Hilbert’s Basis Theorem extends to them. I wi
ll then present generalized nonassociative Ore extensions (GNOEs)\, a natu
ral extension of Ore extensions to the nonassociative setting that provide
s a unifying framework for nonassociative\, noncommutative polynomial ring
s\, including examples such as the Cayley–Dickson algebras. Finally\, I
will show that Hilbert’s Basis Theorem generalizes to GNOEs via the exis
tence of Euclidean division algorithms\, revealing a new and direct connec
tion between such algorithms and the left and right Noetherianity of these
rings. This talk is based on joint work with Masood Aryapoor.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/172/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Radziszewski (University of Białystok\, Poland)
DTSTART:20260511T150000Z
DTEND:20260511T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/173
DESCRIPTION:Title: Affinization of algebraic structures\nby Krzysztof Radziszewski
(University of Białystok\, Poland) as part of European Non-Associative A
lgebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/780318
1064\n\nAbstract\nInformally and in broad terms\, by affinization we mean
a process which converts an algebraic structure with a nullary operation (
i.e. in which a chosen element plays special role) into one which has no n
ullary operations\, but is such that by a free choice of any element it is
retracted to the original structure. The prime example of this procedure
is the conversion of groups into heaps. In this talk we will focus mainly
on affinization of Lie algebras and Leibniz algebras. The talk is based on
joint works with Tomasz Brzeziński\, Ryszard Andruszkiewicz and Brais Ra
mos Perez.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/173/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ágota Figula (University of Debrecen\, Hungary)
DTSTART:20260518T150000Z
DTEND:20260518T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/174
DESCRIPTION:Title: Malcev-like anti-commutative algebras\nby Ágota Figula (Univer
sity of Debrecen\, Hungary) as part of European Non-Associative Algebra Se
minar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nA
bstract\nThe tangent algebras of local analytic Moufang and diassociative
loops are Malcev algebras and binary Lie algebras introduced by A. I. Malc
ev. Their classifications in low dimension are given by the works on E. N.
Kuzmin and A. T. Gainov. In the talk we discuss the classification of sol
vable anti-commutative algebras that have the same decomposition propertie
s as solvable Malcev or binary Lie algebras. The classification result ena
bles us to find and study a family of binary Lie algebras for which the cl
osed form of the Baker-Campbell- Hausdorff series defines the multiplicati
on function of an analytic diassociative loop on the entire binary Lie alg
ebra.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/174/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Pérez-Rodríguez (University of Santiago de Compostela\,
Spain)
DTSTART:20260525T150000Z
DTEND:20260525T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/175
DESCRIPTION:Title: Lattice-theoretical aspects of evolution algebras\nby Andrés P
érez-Rodríguez (University of Santiago de Compostela\, Spain) as part of
European Non-Associative Algebra Seminar\n\nInteractive livestream: https
://us02web.zoom.us/j/7803181064\n\nAbstract\nLattice theories have been de
veloped in several algebraic structures\, such as groups and Lie algebras\
; however\, this is not the case for evolution algebras\, which are commut
ative but nonassociative structures introduced by Tian and Vojtěchovský
in 2006 to model non-Mendelian inheritance. Motivated by this\, in this ta
lk we study the subalgebra lattices of solvable evolution algebras\, focus
ing on two classical lattice-theoretical properties: distributivity and mo
dularity. Subsequently\, we turn to maximal subalgebras\, whose intersecti
on is traditionally known as the Frattini subalgebra. This resulting Fratt
ini theory allows us to investigate intrinsic properties and to characteri
se dually atomistic evolution algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/175/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Powell (University of Angers\, France)
DTSTART:20260921T150000Z
DTEND:20260921T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/176
DESCRIPTION:by Geoffrey Powell (University of Angers\, France) as part of
European Non-Associative Algebra Seminar\n\nInteractive livestream: https:
//us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/176/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Dimitrov (Queen’s University\, Canada)
DTSTART:20260608T150000Z
DTEND:20260608T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/177
DESCRIPTION:Title: U(h)-free modules over the Lie superalgebras sl(m|n)\nby Ivan D
imitrov (Queen’s University\, Canada) as part of European Non-Associativ
e Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/780
3181064\n\nAbstract\nIn this talk I will discuss the existence and classif
ication of certain classes of sl(m|n)-modules which when restricted to the
universal enveloping algebra U(h) of a Cartan subalgebra h are free of fi
nite rank. Particular results include: Classification of modules of rank 2
\; existence and structure of modules of higher rank\; weight modules obta
ined from U(h)-free modules via the weighting functor.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/177/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rinat Kashaev (University of Geneva\, Switzerland)
DTSTART:20260615T150000Z
DTEND:20260615T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/178
DESCRIPTION:Title: Braided Hopf algebra structures on exterior algebras\nby Rinat
Kashaev (University of Geneva\, Switzerland) as part of European Non-Assoc
iative Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/
j/7803181064\n\nAbstract\nThe exterior algebra of any vector space of dime
nsion greater than one admits a one-parameter family of braided Hopf algeb
ra structures\, of which the standard super Hopf algebra structure is a pa
rticular example. By employing a one-parameter family of diagonal automorp
hisms of these braided Hopf algebras\, we construct solutions of the (cons
tant) Yang-Baxter equation. These solutions conjecturally underlie the two
-variable Links-Gould knot invariants associated with quantum supergroups.
This is joint work with Vladimir Mangazeev.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/178/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Cueto-Avellaneda (University of Murcia\, Spain)
DTSTART:20260622T150000Z
DTEND:20260622T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/179
DESCRIPTION:by María Cueto-Avellaneda (University of Murcia\, Spain) as p
art of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/179/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (Istanbul Technical University\, Turkey)
DTSTART:20260706T150000Z
DTEND:20260706T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/180
DESCRIPTION:by Atabey Kaygun (Istanbul Technical University\, Turkey) as p
art of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/180/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Castelli (University of Salento\, Italy)
DTSTART:20260713T150000Z
DTEND:20260713T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/181
DESCRIPTION:Title: The impact of the diagonal permutation on involutive set-theoretic
solutions of the Yang–Baxter Equation\nby Marco Castelli (University
of Salento\, Italy) as part of European Non-Associative Algebra Seminar\n
\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract
\nSince Drinfeld’s 1992 proposal to study the set-theoretic version of t
he Yang–Baxter equation\, involutive solutions have attracted considerab
le attention. It is well known that to every non- degenerate involutive so
lution one can associate a permutation\, referred to in the literature as
the “diagonal permutation”. The aim of this talk is to show how this s
ingle permutation has a strong influence on the structure of (indecomposab
le) involutive set-theoretic solutions. Some of the results presented are
part of a joint work with A. Kanrar.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/181/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marijana Butorac (University of Rijeka\, Croatia)
DTSTART:20260727T150000Z
DTEND:20260727T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/182
DESCRIPTION:Title: Quasi-particle bases of standard modules for affine Lie algebras\nby Marijana Butorac (University of Rijeka\, Croatia) as part of Europea
n Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02w
eb.zoom.us/j/7803181064\n\nAbstract\nCharacters of Feigin-Stoyanovsky's pr
incipal subspaces of affine integrable highest weight modules are related
with the sum sides of Rogers-Ramanujan-type identities. In this talk I w
ill discuss the construction of combinatorial bases of standard modules\,
which relies on the the construction of quasi-particle bases of principal
subspaces. From quasi-particle bases we obtain characters of certain stand
ard modules of affine Lie algebra of type $B_l^{(1)}$. This talk is based
on joint works with Slaven Ko\\v zi\\' c and Mirko Primc.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/182/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Diniz (Federal University of Campina Grande\, Brazil)
DTSTART:20260810T150000Z
DTEND:20260810T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/183
DESCRIPTION:Title: Graded Identities of Finite Matrices\nby Diogo Diniz (Federal U
niversity of Campina Grande\, Brazil) as part of European Non-Associative
Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/78031
81064\n\nAbstract\nPolynomial identities of matrix algebras play a fundame
ntal role in the study of algebraic structures. In this talk\, we focus on
the classification of group gradings on $M_n(F)$\, when $F$ is a finite f
ield\, and on the description of the graded polynomial identities satisfie
d by $M_n(F)$.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/183/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro van Ekeren (Institute of Pure and Applied Mathematics\, Bra
zil)
DTSTART:20260824T150000Z
DTEND:20260824T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/184
DESCRIPTION:Title: Modular data of boundary W-algebras\nby Jethro van Ekeren (Inst
itute of Pure and Applied Mathematics\, Brazil) as part of European Non-As
sociative Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.
us/j/7803181064\n\nAbstract\nThe affine W-algebras form an important class
of infinite dimensional algebras with applications in integrable systems
and geometric representation theory. A special role is played in the theor
y by W-algebras of "boundary level"\, in the sense that certain features o
f the representation theory of W-algebras in general can be determined onc
e the boundary case is understood. I will discuss joint work with T. Araka
wa\, I. Blatt and W.-B. Yan in which we determine the tensor product struc
ture of boundary W-algebras in type A.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/184/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Kinyon (University of Denver\, USA)
DTSTART:20260629T150000Z
DTEND:20260629T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/185
DESCRIPTION:by Michael Kinyon (University of Denver\, USA) as part of Euro
pean Non-Associative Algebra Seminar\n\nInteractive livestream: https://us
02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/185/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannic Vargas (CUNEF University\, Spain)
DTSTART:20260720T150000Z
DTEND:20260720T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/186
DESCRIPTION:by Yannic Vargas (CUNEF University\, Spain) as part of Europea
n Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02w
eb.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/186/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elad Paran (The Open University of Israel\, Israel)
DTSTART:20260803T150000Z
DTEND:20260803T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/187
DESCRIPTION:by Elad Paran (The Open University of Israel\, Israel) as part
of European Non-Associative Algebra Seminar\n\nInteractive livestream: ht
tps://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/187/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Properzi (Vrije Universiteit Brussel\, Belgium)
DTSTART:20261005T150000Z
DTEND:20261005T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/188
DESCRIPTION:by Silvia Properzi (Vrije Universiteit Brussel\, Belgium) as p
art of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/188/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quentin Ehret (New York University Abu Dhabi\, United Arab Emirat
es)
DTSTART:20260907T150000Z
DTEND:20260907T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/189
DESCRIPTION:by Quentin Ehret (New York University Abu Dhabi\, United Arab
Emirates) as part of European Non-Associative Algebra Seminar\n\nInteract
ive livestream: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/189/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lực Ta (University of Pittsburgh\, USA)
DTSTART:20260817T150000Z
DTEND:20260817T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/190
DESCRIPTION:Title: From affine algebraic racks to Leibniz algebras and Yang–Baxter o
perators\nby Lực Ta (University of Pittsburgh\, USA) as part of Euro
pean Non-Associative Algebra Seminar\n\nInteractive livestream: https://us
02web.zoom.us/j/7803181064\n\nAbstract\nA version of Loday's "coquecigrue"
problem over arbitrary ground fields seeks analogues of affine algebraic
groups whose tangent spaces are Leibniz algebras. To that end\, we constru
ct functors assigning left and right Leibniz algebras to pointed rack obje
cts in the category of affine schemes. These functors have many desirable
properties\; in particular\, they recover the Lie algebras of linear algeb
raic groups (via conjugation quandles) and the Leibniz algebras of algebra
ic Lie racks. We also use rack schemes to functorially construct (co-)nond
egenerate solutions to the Yang–Baxter equation in the categories of sch
emes\, sets\, and commutative k-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/190/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Albano (University of Salento\, Italy)
DTSTART:20260323T150000Z
DTEND:20260323T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/191
DESCRIPTION:Title: Set-theoretic solutions of the Yang--Baxter equation and di-skew br
aces.\nby Andrea Albano (University of Salento\, Italy) as part of Eur
opean Non-Associative Algebra Seminar\n\n\nAbstract\nThe aim of this talk
is to provide a brief overview of the role of generalised digroups in the
study of the set-theoretic Yang-Baxter equation (YBE). Digroups are algebr
aic objects endowed with two binary associative operations that arose in t
he investigations of R. Felipe\, K. Liu and M. Kinyon around the so-called
coquecigrue problem\, as first stated by J. L. Loday. In detail\, we will
introduce the structure of di-skew braces as a split notion of usual skew
braces and show how they provide a class of non-degenerate solutions to t
he set-theoretic YBE whose (left) derived rack is not necessarily idempote
nt. Moreover\, we will describe basic properties of such solutions through
the lens of self-distributivity and explore related ideas. Based on a joi
nt work with Paola Stefanelli.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Trombetti (University of Naples Federico II\, Italy)
DTSTART:20260601T150000Z
DTEND:20260601T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/192
DESCRIPTION:Title: On Cardinalities whose Arithmetical Properties Determine the Struct
ure of Solutions of the Yang--Baxter Equation\nby Marco Trombetti (Uni
versity of Naples Federico II\, Italy) as part of European Non-Associative
Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803
181064\n\nAbstract\nWe provide purely arithmetical characterisations of th
ose natural numbers n for which every non-degenerate set-theoretic solutio
n of cardinality n of the Yang--Baxter equation arising from a skew brace
(sb-solution for short) satisfies some relevant properties\, such as being
a flip\, involutive\, or multipermutation. This is based on joint work wi
th M. Ferrara and C. Tsang.\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/192/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inna Entova-Aizenbud (Ben Gurion University of the Negev\, Israel)
DTSTART:20261109T150000Z
DTEND:20261109T160000Z
DTSTAMP:20260407T225205Z
UID:ENAAS/193
DESCRIPTION:by Inna Entova-Aizenbud (Ben Gurion University of the Negev\,
Israel) as part of European Non-Associative Algebra Seminar\n\nInteractive
livestream: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ENAAS/193/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
END:VCALENDAR