BEGIN:VCALENDAR
VERSION:2.0
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Zerui Zhang (South China Normal University\, China)
DTSTART:20221226T080000Z
DTEND:20221226T090000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/1
DESCRIPTION:Title: Some results on Novikov algebras and Novikov-Poisson alge
bras\nby Zerui Zhang (South China Normal University\, China) as part o
f Non-Associative Day in Online\n\n\nAbstract\nWe first prove that a left
Novikov algebra is right nilpotent if and only if it is solvable. And we s
how that the ideal generated by all the commutators of a Lie nilpotent Nov
ikov algebra is nilpotent. Then a connection between Novikov algebras and
differential commutative algebras will be discussed. Finally\, we show tha
t such a connection have an analogue between unital Novikov-Poisson algebr
as and special Novikov-Poisson admissible algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiefeng Liu (Northeast Normal University\, China)
DTSTART:20221226T090000Z
DTEND:20221226T100000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/2
DESCRIPTION:Title: Cohomology and deformation quantization of Poisson confor
mal algebras\nby Jiefeng Liu (Northeast Normal University\, China) as
part of Non-Associative Day in Online\n\n\nAbstract\nIn this talk\, we fir
st recall the notion of (noncommutative) Poisson conformal algebras and gi
ve some constructions of them. Then we introduce the notion of conformal f
ormal deformations of commutative associative conformal algebras and show
that Poisson conformal algebras are the corresponding semi-classical limit
s. At last\, we develop the cohomology theory of noncommutative Poisson co
nformal algebras and use this cohomology to study their deformations.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengming Bai (Nankai University\, China)
DTSTART:20221226T100000Z
DTEND:20221226T110000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/3
DESCRIPTION:Title: Parity duality of super r-matrices via O-operators and pr
e-Lie superalgebras\nby Chengming Bai (Nankai University\, China) as p
art of Non-Associative Day in Online\n\n\nAbstract\nWe interpret the homog
eneous solutions of the super classical Yang-Baxter equation\, also called
super r-matrices\, in terms of O-operators by a unified treatment. Furthe
rmore\, by a parity reversion of Lie superalgebra representations\, a dual
ity is established between the even and odd O-operators. This leads to a p
arity duality of the super r-matrices induced by the O-operators in semi-d
irect product Lie superalgebras. Therefore a pre-Lie superalgebra naturall
y defines an even O-operator\, and hence an odd O-operator by the duality\
, thereby giving rise to a parity pair of super r-matrices. This is a join
t work with Li Guo and Runxuan Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangui Zhao (Huizhou University\, China)
DTSTART:20221226T120000Z
DTEND:20221226T130000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/4
DESCRIPTION:Title: Growth and Gelfand-Kirillov dimension of brace algebras\nby Xiangui Zhao (Huizhou University\, China) as part of Non-Associativ
e Day in Online\n\n\nAbstract\nA brace algebra over a field is a vector sp
ace equipped with a family of linear operations satisfying certain identit
ies. Brace algebras have strong connections with other important classes o
f algebras such as pre-Lie algebras\, ε-bialgebras\, and dendriform algeb
ras. The Gelfand-Kirillov dimension of a (not necessarily associative) alg
ebra is an important invariant for the study of the growth of the algebra.
In this talk\, we discuss the growth and possible values of the Gelfand-K
irillov dimension of brace algebras. In particular\, we construct examples
to show that the Bergman's gap theorem for the Gelfand-Kirillov dimension
of associative algebras does not hold for brace algebras. This is joint w
ork with Qiuhui Mo\, Yu Li\, and Wenchao Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farkhod Eshmatov (AKFA University\, Uzbekistan)
DTSTART:20221226T130000Z
DTEND:20221226T140000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/5
DESCRIPTION:Title: Necklace Lie algebra and derived Poisson structure\nb
y Farkhod Eshmatov (AKFA University\, Uzbekistan) as part of Non-Associati
ve Day in Online\n\n\nAbstract\nWe introduce the notion of a derived Poiss
on structure on an associative (not necessarily commutative) algebra. Then
we will discuss how Necklace Lie algebra structure can be used to constru
ct derived Poisson bracket for some interesting classes of algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uzi Vishne (Bar Ilan University\, Israel)
DTSTART:20221226T140000Z
DTEND:20221226T150000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/6
DESCRIPTION:Title: Identities of the tensor square of the octonion algebra\nby Uzi Vishne (Bar Ilan University\, Israel) as part of Non-Associativ
e Day in Online\n\n\nAbstract\nWe describe the nonassociative polynomial i
dentities of minimal degree\, which is 7\, for the algebras $\\mathcal O \
\times \\mathcal O$ and ${\\rm M}_2(\\mathcal O)\,$ where $\\mathcal O$ is
the octonion algebra. After being discovered by a computer\, the proofs a
re rather elegant. We also discuss some related open problems on varieties
of nonassociative algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fox (Polytechnic University of Madrid\, Spain)
DTSTART:20221226T160000Z
DTEND:20221226T170000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/7
DESCRIPTION:Title: Sectional nonassociativity of metrized algebras\nby D
aniel Fox (Polytechnic University of Madrid\, Spain) as part of Non-Associ
ative Day in Online\n\n\nAbstract\nThe sectional nonassociativity of a met
rized (not necessarily associative or unital) algebra is defined analogous
ly to the sectional curvature of a pseudo-Riemannian metric\, with the ass
ociator in place of the Levi-Civita covariant derivative. For commutative
real algebras nonnegative sectional nonassociativity is usually called the
Norton inequality\, while a sharp upper bound on the sectional nonassocia
tivity of the Jordan algebra of Hermitian matrices over a real Hurwitz alg
ebra is closely related to what is known as the Böttcher-Wenzel-Chern-do
Carmo-Kobayashi inequality. These and other basic examples are explained\,
and there are described some consequences of bounds on sectional nonassoc
iativity for commutative algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xingting Wang (Howard University\, USA)
DTSTART:20221226T170000Z
DTEND:20221226T180000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/8
DESCRIPTION:Title: Twisting of graded quantum groups and solutions to the qu
antum Yang-Baxter equation\nby Xingting Wang (Howard University\, USA)
as part of Non-Associative Day in Online\n\n\nAbstract\nLet $H$ be a Hopf
algebra over a field $k$ such that $H$ is $\\mathbb Z$-graded as an algeb
ra. In this talk\, we introduce the notion of a twisting pair for $H$ and
show that the Zhang twist of $H$ by such a pair can be realized as a $2$-c
ocycle twist. We use twisting pairs to describe twists of Manin’s univer
sal quantum groups associated to quadratic algebras. Furthermore\, we disc
uss a strategy to twist a solution to the quantum Yang-Baxter equation via
the Faddeev-Reshetikhin-Takhtajan construction. If time permits\, we illu
strate this result for the quantized coordinate rings of ${\\rm GL}_n(k)$.
This is joint work with Hongdi Huang\, Van Nguyen\, Charlotte Ure\, Kent
Vashaw and Padmini Veerapen.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Guo (Rutgers University\, USA)
DTSTART:20221226T180000Z
DTEND:20221226T190000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/9
DESCRIPTION:Title: Coherent categorical structures for Lie bialgebras\, Mani
n triples\, classical r-matrices and pre-Lie algebras\nby Li Guo (Rutg
ers University\, USA) as part of Non-Associative Day in Online\n\n\nAbstra
ct\nThe broadly applied notions of Lie bialgebras\, Manin triples\, classi
cal r-matrices and O-operators of Lie algebras owe their importance to the
close relationship among them. Yet these notions and their correspondence
s are mostly understood as classes of objects and maps among the classes.
To gain categorical insight\, we introduce\, for each of the classes\, a n
otion of homomorphisms\, uniformly called coherent homomorphisms\, so that
the classes of objects become categories and the maps among the classes b
ecome functors or category equivalences. For this purpose\, we start with
the notion of an endo Lie algebra\, consisting of a Lie algebra equipped w
ith a Lie algebra endomorphism. We then generalize the above classical not
ions for Lie algebras to endo Lie algebras. As a result\, we obtain the no
tion of coherent endomorphisms for each of the classes\, which then genera
lizes to the notion of coherent homomorphisms by a polarization process. T
he coherent homomorphisms are compatible with the correspondences among th
e various constructions\, as well as with the category of pre-Lie algebras
. This is a joint work with Chengming Bai and Yunhe Sheng.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Askar Dzhumadil'daev (Institute of Mathematics and Mathematical Mo
deling\, Kazakhstan)
DTSTART:20231218T070000Z
DTEND:20231218T080000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/10
DESCRIPTION:Title: Rota-Baxter algebras with non-zero weights\nby Askar
Dzhumadil'daev (Institute of Mathematics and Mathematical Modeling\, Kaza
khstan) as part of Non-Associative Day in Online\n\n\nAbstract\nFor an ass
ociative commutative algebra $A$ with Rota-Baxter operator $R : A \\to A$
with weight $\\lambda$ denote by $AR$ an algebra with linear space $A$ and
multiplication $a \\circ b = aR(b)$. Let $AR^{−}$ and $AR^{+}$ are alge
bra $AR$ under Lie and Jordan commutators. If $\\lambda = 0$\, then the al
gebra $AR = (A\, \\circ)$ is Zinbiel\, $AR^{+}$ is associative\, and $AR^{
−}$ is Tortkara. We find polynomial identities of algebras $AR$\, $AR^{
−}$ and $AR^{+}$ in case $\\lambda \\neq0$. We prove that $AR^{−}$ i
s Tortkara. $AR^{+}$ satisfies an identity of degree $5$. In case $\\lambd
a \\neq 0$\, the algebra $AR$ is not associative-admissible.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ievgen Makedonskyi (Beijing Institute of Mathematical Scienses and
applications\, China)
DTSTART:20231218T090000Z
DTEND:20231218T100000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/11
DESCRIPTION:Title: Duality Theorems for current Lie algebras\nby Ievgen
Makedonskyi (Beijing Institute of Mathematical Scienses and applications\
, China) as part of Non-Associative Day in Online\n\n\nAbstract\nWe study
some natural representations of current Lie algebras\, called Weyl modules
. They are natural analogues of irreducible representations of simple Lie
algebras. There are several current analogues of classical theorems about
Lie algebras where these modules «play role» of irreducible modules. In
my talk\, I will explain analogues of duality theorems\, namely Peter-Weyl
theorem\, Schur-Weyl duality etc.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Kolesnikov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20231218T110000Z
DTEND:20231218T120000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/12
DESCRIPTION:Title: Derived nonassociative algebras: identities and embeddin
g problem\nby Pavel Kolesnikov (Sobolev Institute of Mathematics\, Rus
sia) as part of Non-Associative Day in Online\n\n\nAbstract\nGiven a nonas
sociative algebra A with a derivation d\, let us define its derived algebr
a as the same linear space A equipped with two operations of multiplicatio
n \na$<$b=ad(b)\, a$>$b=d(a)b\, for a\,b in A. The purpose of this talk is
to show how to derive the identities that hold on all such derived algebr
as provided that A ranges through a given variety of nonassociative algebr
as. (In particular\, for the variety of associative and commutative algeb
ras the result is very well known: the variety of Novikov algebras appears
in this way.) We also study the natural embedding problem related to the
functor transforming a differential algebra into its derived algebra. We s
tate a sufficient condition that guarantees an affirmative answer to the e
mbedding problem and show an example when the embedding problem has a nega
tive solution.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Viruel (University of Malaga\, Spain)
DTSTART:20231218T120000Z
DTEND:20231218T130000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/13
DESCRIPTION:Title: Permutation represention of finite groups via automorphi
sms of idempotent evolution algebras\nby Antonio Viruel (University of
Malaga\, Spain) as part of Non-Associative Day in Online\n\n\nAbstract\nI
n the wake of the influential work by Elduque-Labra\, it is known that eve
ry finite dimensional evolution K-algebra X such that X^2=X\, namely X is
idempotent\, has finite group of automorphisms. Building on this foundati
on\, works of Costoya et al. show that given any finite group G\, there ex
ists an idempotent finite-dimensional evolution algebra X such that Aut(X
)\\cong G. Moreover\, when the base field is sufficiently large in compari
son to the group G\, such an X can be selected to be simple. As a result\
, Sriwongsa-Zou propose that idempotent finite-dimensional evolution algeb
ras can be classified based on the isomorphism type of their group of auto
morphisms and dimension. Within this context\, we establish that the natur
al representation of highly transitive groups cannot be realized as the co
mplete group of automorphisms of an idempotent finite-dimensional evolutio
n algebra. For instance\, for any sufficiently large integer n\, there exi
sts no evolution algebra X such that X^2=X\, dim X=n\, and Aut(X) is isomo
rphic to the alternating group A_n. However\, we demonstrate that for any
(not necessarily faithful) permutation representation p : G -> S_n and any
field K\, there exists a finite-dimensional evolution K-algebra X such th
at X^2=X\, Aut(X)\\cong G$ and the induced representation given by the Aut
(X)-action on the natural idempotents of X is p. This is a joint work with
C. Costoya (U. Santiago Compostela) and Pedro Mayorga (U. Malaga).\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Mathieu (University of Lyon\, France)
DTSTART:20231218T130000Z
DTEND:20231218T140000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/14
DESCRIPTION:Title: On free Jordan Algebras\nby Olivier Mathieu (Univers
ity of Lyon\, France) as part of Non-Associative Day in Online\n\n\nAbstra
ct\nThe free Jordan algebra J(m) on m generators is an elusive object. It
has been determined when m=1 (folklore) and m=2 (Shirshov’s Theorem). So
me partial informations are known in the case m=3\, namely the space of Jo
rdan polynomial with three variables which are linear on the last one. We
will present two conjectures. Conjecture 1\, which determines combinatoria
lly the structure of the homogenous components of J(m) is elementary but m
ysterious. Then we present Conjecture 2 about Lie algebra cohomology of a
class of free Lie algebras in a certain category. Conjecture 2 is natural\
, but not elementary. Our main result is that Conjecture 2 implies Conject
ure 1. The proof\, which is quite long\, is based on the cyclicity of the
Jordan operad. Conjecture 1 has been checked up to degree 15 for m=2\, up
to degree 7 for m=3 and up to degree 6 for m>3. In the case m=1\, the conj
ecture is equivalent to Jacobi triple identity. For conjecture 2\, the van
ishing of the cohomology has been proved up to degree 3 using polynomial f
unctors. In a recent work with J. Germoni\, we found two new special ident
ities in degree 8 and 4 variables. These identities have been checked by c
omputer\, but the interesting point is that they were predicted by our con
jecture.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom De Medts (Ghent University\, Belgium)
DTSTART:20231218T150000Z
DTEND:20231218T160000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/15
DESCRIPTION:Title: Primitive axial algebras of Jordan type and 3-transposit
ion groups\nby Tom De Medts (Ghent University\, Belgium) as part of No
n-Associative Day in Online\n\n\nAbstract\nThe classification of 3-transpo
sition groups has a long history. In particular\, it is a highly non-trivi
al fact that finitely generated 3-transposition groups are finite. We prov
ide an alternative viewpoint on this question using the corresponding “M
atsuo algebras”\, a class of non-associative algebras. These are instanc
es of primitive axial algebras of Jordan type. We prove that primitive 4-g
enerated axial algebras of Jordan type are at most 81-dimensional (and thi
s bound is sharp). This is joint work with Louis Rowen and Yoav Segev (to
appear in Proc. AMS).\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Shpectorov (University of Birmingham\, UK)
DTSTART:20231218T160000Z
DTEND:20231218T170000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/16
DESCRIPTION:Title: Solid subalgebras in algebras of Jordan type half\nb
y Sergey Shpectorov (University of Birmingham\, UK) as part of Non-Associa
tive Day in Online\n\n\nAbstract\nAlgebras of Jordan type $\\eta$ generali
se in the axial context the class of Jordan algebras generated \nby primit
ive idempotents. In addition to these examples\, arising for $\\eta=\\frac
{1}{2}$\, the class of \nalgebras of Jordan type includes the Matsuo algeb
ras\, constructed in terms of $3$-transposition groups \nfor all values of
$\\eta$. Classification of algebras of Jordan type for $\\eta\\neq\\frac{
1}{2}$ was completed \nby Hall\, Rerhen and Shpectorov in 2015\, with a co
rrection by Hall\, Segev and Shpectorov in 2018. The \ncase of $\\eta=\\fr
ac{1}{2}$ remains open.\n\nAmong the known results about algebras of Jorda
n type half are the classification\, in the above mentioned \npaper from 2
015\, of $2$-generated algebras\, the classification of $3$-generated alge
bras by Gorshkov \nand Staroletov in 2020\, and the recent (from 2023) res
ult by De Medts\, Rowen and Segev bounding the \ndimension of $4$-generate
d algebras by $81$.\n\nIn the talk we will discuss another recent (in prep
aration\, 2023) result on the subject\, by Gorshkov\, \nStaroletov and Shp
ectorov. A $2$-generated subalgebra $B$ of an algebra $A$ of Jordan type h
alf is called \n\\emph{solid} if every primitive idempotent from $B$ is an
axis in the entire $A$. Surprisingly\, it turned \nout that\, at least in
characteristic zero\, almost all $2$-generated subalgebras are solid. Mor
e\, precisely\, \na non-solid $2$-generated subalgebra is necessarily of t
ype $3C(\\frac{1}{2})$. Consequently\, if a \nfinite-dimensional algebras
of Jordan type half has a finite automorphism group then it is either a Ma
tsuo \nalgebra or a factor of Matsuo algebra.\n\nThe above result hints of
a possibility of a geometric theory of algebras of Jordan type half.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Gaddis (Miami University\, USA)
DTSTART:20231218T170000Z
DTEND:20231218T180000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/17
DESCRIPTION:Title: Rigidity of quadratic Poisson algebras\nby Jason Gad
dis (Miami University\, USA) as part of Non-Associative Day in Online\n\n\
nAbstract\nThe Shephard-Todd-Chevalley Theorem gives conditions for the in
variant ring of a polynomial ring to again be polynomial. However\, this b
ehavior is rarely observed for noncommutative algebras. For example\, the
invariant ring of the first Weyl algebra by a finite group is not isomorph
ic to the first Weyl algebra. In this talk\, I will discuss this rigidity
in the context of quadratic Poisson algebras. A key example will be those
Poisson polynomial algebras with skew-symmetric structure. This is joint w
ork with Padmini Veerapen and Xingting Wang.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences\, Bulgaria)
DTSTART:20231218T080000Z
DTEND:20231218T090000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/18
DESCRIPTION:Title: The Specht problem for varieties of Z n -graded Lie alge
bras in positive characteristic\nby Vesselin Drensky (Institute of Mat
hematics and Informatics\, Bulgarian Academy of Sciences\, Bulgaria) as pa
rt of Non-Associative Day in Online\n\n\nAbstract\nLet K be a field of pos
itive characteristic p and let UT p+1 (K) be the algebra of (p+1)×(p+1) u
pper triangular matrices. We construct three varieties of Z p+1 -graded Li
e algebras which do not have a finite basis of their graded identities and
satisfy the graded identities which in the case of infinite field define
the variety generated by UT p+1 (K). The first variety contains the other
two. The second one is locally finite. The third variety is generated by a
finite dimensional algebra over an infinite field. These results are in t
he spirit of similar results obtained in the 1970s and 1980s for non-grade
d Lie algebras in positive characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhanqiang Bai (Soochow University\, China)
DTSTART:20241223T080000Z
DTEND:20241223T090000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/19
DESCRIPTION:Title: Gelfand-Kirillov dimensions of highest weight modules of
simple Lie algebras\nby Zhanqiang Bai (Soochow University\, China) as
part of Non-Associative Day in Online\n\n\nAbstract\nGelfand-Kirillov dim
ension is an important invariant\, which was introduced by Gelfand and Kir
illov in 1960s. This invariant usually can measure the size of the infinit
e-dimensional algebraic structures. In this talk\, by using Lusztig's a-fu
nction and based on our previous work\, we will give an algorithm to comp
ute the Gelfand-Kirillov dimensions of highest weight modules of exception
al type Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cindy Tsang (Ochanomizu University in Tokyo\, Japan)
DTSTART:20241223T090000Z
DTEND:20241223T100000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/20
DESCRIPTION:Title: On Grün's lemma for perfect skew braces\nby Cindy T
sang (Ochanomizu University in Tokyo\, Japan) as part of Non-Associative D
ay in Online\n\n\nAbstract\nThe well-known Grün’s lemma in group theory
states that the quotient of a perfect group by its center is always cente
rless. In this talk\, we shall consider its analog in the setting of skew
brace\, an algebraic structure that was introduced in the study of set-the
oretic solutions to the Yang-Baxter equation. Here we shall use the annihi
lator of a skew brace as an analog of the center of a group. Our main res
ult is that the analog of Grün’s lemma always holds for two-sided perfe
ct skew braces but fails in general.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Centrone (University of Bari\, Italy)
DTSTART:20241223T100000Z
DTEND:20241223T110000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/21
DESCRIPTION:Title: On geometries arising from varieties of algebras\nby
Lucio Centrone (University of Bari\, Italy) as part of Non-Associative Da
y in Online\n\n\nAbstract\nWe will construct geometric objects via varieti
es of algebras and we shall see how they interplay in the light of their p
olynomial identities.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kurusch Ebrahimi-Fard (Norwegian University of Science and Technol
ogy\, Norway)
DTSTART:20241223T120000Z
DTEND:20241223T130000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/22
DESCRIPTION:Title: A post-group theoretic perspective on the operator-value
d S-transform in free probability\nby Kurusch Ebrahimi-Fard (Norwegian
University of Science and Technology\, Norway) as part of Non-Associative
Day in Online\n\n\nAbstract\nWe discuss the algebraic structure underlyin
g Voiculescu's S-transform in operator-valued free probability. It is show
n how its twisted factorisation property gives rise to post-groups\, cross
ed morphisms\, as well as pre- and post-Lie algebras. Based on joint work
with T. Ringeard (arXiv:2402.16450).\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahender Singh (IISER Mohali\, India)
DTSTART:20241223T130000Z
DTEND:20241223T140000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/23
DESCRIPTION:Title: Idempotents of quandle rings and application to knots\nby Mahender Singh (IISER Mohali\, India) as part of Non-Associative Day
in Online\n\n\nAbstract\nQuandles are non-associative algebraic structure
s arising from the algebraic formulation of the Reidemeister moves of plan
ar diagrams of knots. Quandle rings were introduced recently as analogues
of group rings for quandles. In this talk\, we will explore the idempotent
s of quandle rings and their connection to quandle coverings. We show that
integral quandle rings of finite-type quandles\, which are non-trivial co
verings of well-behaved base quandles\, possess infinitely many non-trivia
l idempotents\, and offer a complete characterization of these idempotents
. Additionally\, we show that integral quandle rings of free quandles cont
ain only trivial idempotents\, thereby identifying an infinite family of q
uandles with this property. In terms of applications to knot theory\, we p
resent explicit examples of knots where coloring with idempotents yields s
tronger invariants compared to the traditional quandle coloring invariant.
\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Peralta (University of Granada\, Spain)
DTSTART:20241223T140000Z
DTEND:20241223T150000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/24
DESCRIPTION:Title: Maps preserving $\\lambda$-Aluthge transforms on product
\nby Antonio Peralta (University of Granada\, Spain) as part of Non-As
sociative Day in Online\n\n\nAbstract\nGiven $\\lambda \\in[0\,1]\,$ the \
\emph{$\\lambda$-Aluthge transform} of an element $a$ in a von Neumann alg
ebra $M$ is defined by $\\Delta_{\\lambda}(a)=|a|^{\\lambda} u |a|^{1-\\la
mbda}\,$ where $a = u |a|$ is the polar decomposition of $a$ in $M$. This
talk will be devoted to survey some of the main conclusions on bijective m
aps between von Neumann algebras commuting with the $\\lambda$-Aluthge tra
nsform on products of the form $a b$\, $ab^*$\, $a\\circ b$ and $a\\circ b
^*$\, where $\\circ$ denotes the natural Jordan product. We shall show tha
t all these maps are naturally linked to the Jordan structure of the von N
eumann algebras. We shall also see how these problems are naturally connec
ted with those classical studies by J. Hakeda and K. Saito on linear bijec
tions between von Neumann algebras preserving products of the form $a b$ a
nd $a\\circ b$.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriy Bardakov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20241223T160000Z
DTEND:20241223T170000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/25
DESCRIPTION:Title: Rota-Baxter operators on groups\, ranks\, and algebras\nby Valeriy Bardakov (Sobolev Institute of Mathematics\, Russia) as par
t of Non-Associative Day in Online\n\n\nAbstract\nRota--Baxter operators (
RB-operators) for commutative algebras were introduced by Baxter in 1960.
Since then\, the theory of Rota-Baxter operators has undergone extensive d
evelopment by various authors in different fields of mathematics. In 2021
L. Guo\, H. Lang\, and Y. Sheng defined a Rota--Baxter operator on groups
and proved that if $G$ is a Lie group and $B \\colon G \\to G$ is a Rota--
Baxter operator\, then the tangent map $B$ at identity is a Rota--Baxter o
perator on the Lie algebra of $G$. In 2024 V.G. Bardakov and V.A. Bovdi
introduced Rota--Baxter operators on racks and quandles. In my talk\, I w
ill give a survey of results that we have found with my colleagues during
the last few years and which are dedicated to RB--operators on groups\, r
acks\, and Hopf algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Zhang (University of Washington\, USA)
DTSTART:20241223T180000Z
DTEND:20241223T190000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/26
DESCRIPTION:Title: Poisson valuations and applications\nby James Zhang
(University of Washington\, USA) as part of Non-Associative Day in Online\
n\n\nAbstract\nWe introduce the notation of a Poisson valuation and use it
to study automorphism\, isomorphism\, and embedding problems for several
classes of Poisson algebras/fields. This is joint work with Hongdi Huang\,
Xin Tan\, and Xingting Wang\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Gateva-Ivanova (American University in Bulgaria\, Bulgaria
)
DTSTART:20241223T170000Z
DTEND:20241223T180000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/27
DESCRIPTION:Title: Quadratic algebras and idempotent braided sets\nby T
atiana Gateva-Ivanova (American University in Bulgaria\, Bulgaria) as part
of Non-Associative Day in Online\n\n\nAbstract\nWe study the Yang-Baxter
algebras $A(K\,X\,r)$ associated to finite set-theoretic solutions $(X\,r)
$ of the braid relations. We introduce an equivalent set of quadratic rela
tions $R \\subseteq G$\, where $G$ is the reduced Gr\\"{o}bner basis of $R
$. We show that if $(X\,r)$ is left-nondegenerate and idempotent then $R=G
$ and the Yang-Baxter algebra is PBW. We use graphical methods to study th
e global dimension of n-generated PBW algebras in the general case and app
ly this to Yang-Baxter algebras in the left-nondegenerate idempotent case.
We study the d-Veronese subalgebras for a class of quadratic algebras and
use this to show that for $(X\,r)$ left-nondegenerate idempotent\, the d-
Veronese subalgebra $A^{(d)}$ of $A =A(K\,X\,r)$ can be identified with $A
(K\,X\,r^{(d)})$\, where $(X\,r^{(d)})$ are left-nondegenerate idempotent
solutions for all $d \\geq 2$. We determined the Segre product in the left
-nondegenerate idempotent setting. Our results apply to a previously studi
ed class of `permutation idempotent' solutions\, where we show that all th
eir Yang-Baxter algebras for a given cardinality of $X$ are isomorphic and
are isomorphic to their d-Veronese subalgebras. In the linearised setting
\, we construct the Koszul dual of the Yang-Baxter algebra and the Nichols
-Woronowicz algebra in the idempotent case\, showing that the latter is qu
adratic. We also construct noncommutative differentials on some of these q
uadratic algebras. This talk is based on a joint work with Shahn Majid.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bauyrzhan Sartayev (Narxoz University\, Kazakhstan)
DTSTART:20251222T080000Z
DTEND:20251222T090000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/28
DESCRIPTION:Title: On the Malcev classification for the variety of associat
ive algebras\nby Bauyrzhan Sartayev (Narxoz University\, Kazakhstan) a
s part of Non-Associative Day in Online\n\n\nAbstract\nIn this talk\, we c
onsider four types of subvarieties of the variety of associative algebras.
We study these subvarieties from the point of view of operads and show th
eir connections with well-known classes of algebras\, such as dendriform a
lgebras and noncommutative Novikov algebras. Also\, we define the commutat
or and anti-commutator operations on these algebras and derive several ide
ntities satisfied by these operations. For the second and third types of a
ssociative algebras\, we construct the bases for the corresponding free al
gebras. Finally\, we prove that a free metabelian Lie algebra can be embe
dded into a free associative algebra of the second type.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solomon Vishkautsan (Tel-Hai Academic College\, Israel)
DTSTART:20251222T090000Z
DTEND:20251222T100000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/29
DESCRIPTION:Title: Eigenvalues and linear recurrence relations over the Oct
onions\nby Solomon Vishkautsan (Tel-Hai Academic College\, Israel) as
part of Non-Associative Day in Online\n\n\nAbstract\nI will discuss joint
work with Adam Chapman and Ilan Levin\, regarding algorithms for: finding
left/right eigenvalues of Octonion matrices (2x2 so far)\, and solving lin
ear recurrences of order 2 over the Octonions.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Kolesnikov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20251222T100000Z
DTEND:20251222T110000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/30
DESCRIPTION:Title: Dendriform splitting and chiral algebras\nby Pavel K
olesnikov (Sobolev Institute of Mathematics\, Russia) as part of Non-Assoc
iative Day in Online\n\n\nAbstract\nVertex algebras usually considered as
a tool in mathematical physics (conformal field theory) or representation
theory (infinite-dimensional Lie algebras and sporadic finite simple group
s) may be thought of as of deeply generalized analogues of Poisson algebra
s. Namely\, following B. Bakalov and V.G. Kac (2002)\, a vertex algebra is
a breed of pre-Lie differential algebra and Lie conformal algebra structu
res. In this talk\, we will observe several approaches to vertex algebras
including the one via chiral operads. Within the latter approach\, a verte
x algebra is a morphism from the operad Lie to the chiral operad P^{ch}(V)
constructed on a space V with a single linear operator. We apply this app
roach to get the class of dendriform split systems (preLie chiral\, or pre
-vertex algebras) and study the left adjoint functor to the forgetful func
tor from the category of pre-vertex algebras to preLie conformal algebras.
\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Centrone (University of Bari\, Italy)
DTSTART:20251222T120000Z
DTEND:20251222T130000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/31
DESCRIPTION:Title: On algebras with regular gradings\nby Lucio Centrone
(University of Bari\, Italy) as part of Non-Associative Day in Online\n\n
\nAbstract\nWe will show the latest results on algebras endowed with a reg
ular grading.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cindy Tsang (Ochanomizu University in Tokyo\, Japan)
DTSTART:20251222T130000Z
DTEND:20251222T140000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/32
DESCRIPTION:Title: Hopf--Galois structures of cyclic type on parallel exten
sions of prime power degree\nby Cindy Tsang (Ochanomizu University in
Tokyo\, Japan) as part of Non-Associative Day in Online\n\n\nAbstract\nLet
$L/K$ be a finite separable extension with Galois closure $\\widetilde{L}
/K$. We say that $L'/K$ is parallel to $L/K$ if $L'$ is an immediate field
of $\\widetilde{L}/K$ and $[\\widetilde{L}:K]=[L:K]$. Note that this noti
on is not symmetric. We are interested in comparing the Hopf-Galois struct
ures on $L'/K$ with those on $L/K$. In this talk\, I will first explain ho
w this problem reduces to a completely group-theoretic problem that involv
es the study of transitive subgroups of the holomorph. After that\, I will
report on some new results when the type of the Hopf-Galois structures is
cyclic and the degree of the extension is a prime power. This is joint wo
rk with Andrew Darlington.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Doikou (Heriot-Watt University\, UK)
DTSTART:20251222T140000Z
DTEND:20251222T150000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/33
DESCRIPTION:Title: Combinatorial Drinfel'd twists & the Yang-Baxter equatio
n\nby Anastasia Doikou (Heriot-Watt University\, UK) as part of Non-As
sociative Day in Online\n\n\nAbstract\nWe introduce the special set-theore
tic Yang-Baxter algebra and show that it is a Hopf algebra subject to cert
ain conditions. The associated universal R-matrix is also obtained via an
admissible Drinfel'd twist. The structure of braces emerges naturally in t
his context by requiring the special set-theoretic Yang-Baxter algebra to
be a Hopf algebra and a quasi-triangular bialgebra after twisting. The fun
damental representation of the universal R-matrix yields the familiar invo
lutive set-theoretic (combinatorial) solution of the Yang-Baxter equation.
We also introduce rack Hopf-like algebras and obtain rack and quandle so
lutions of the YBE. We show that the same combinatorial twist cane be used
to produce non-involutive set-theoretic solutions.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marzia Mazzotta (University of Salento\, Italy)
DTSTART:20251222T160000Z
DTEND:20251222T170000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/34
DESCRIPTION:Title: Associative Pentagon Algebras\nby Marzia Mazzotta (U
niversity of Salento\, Italy) as part of Non-Associative Day in Online\n\n
\nAbstract\nA set-theoretical solution of the Pentagon Equation can be des
cribed in terms of a \\emph{pentagon algebra} $(S\, +\, \\ast)$\, namely\
, a set equipped with two binary operations where $(S\,+)$ forms a semigro
up and the operations $+$ and $\\ast$ satisfy additional compatibility con
ditions arising from the Pentagon Equation. In this talk\, we introduce an
algebraic framework for studying such structures and outline several stra
tegies for constructing and classifying their solutions. Our attention wil
l be devoted in particular to the case in which the second operation $\\as
t$ is also associative. We present characterizations of these algebras\, t
ogether with structural consequences for the interaction between the two o
perations. Moreover\, we will present some recent results from an ongoing
collaboration with Agata Pilitowska and Arne Van Antwerpen.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fairon (Université Bourgogne Europe\, France)
DTSTART:20251222T170000Z
DTEND:20251222T180000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/35
DESCRIPTION:Title: Double Poisson algebra cohomology\nby Maxime Fairon
(Université Bourgogne Europe\, France) as part of Non-Associative Day in
Online\n\n\nAbstract\nThe structure of a double Poisson algebra (as introd
uced by Van den Bergh) induces a structure of Poisson algebra on each of i
ts representation algebras. For these\, a cohomology theory (initiated by
Pichereau and Van de Weyer) can be constructed under mild conditions\, and
it gets mapped to the usual Poisson cohomology of the corresponding repre
sentation algebras. My aim is to recall this original construction\, and t
hen I will explain a far-reaching generalisation leading to several other
cohomology theories of a similar nature. This talk is meant to be an overv
iew of Part 1 of arXiv:2509.21232 (joint with Daniele Valeri).\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Lopatin (University of Campinas\, Brazil)
DTSTART:20251222T180000Z
DTEND:20251222T190000Z
DTSTAMP:20260404T111110Z
UID:NonAssociativeDay/36
DESCRIPTION:Title: Invariants for simple evolution algebras\nby Artem L
opatin (University of Campinas\, Brazil) as part of Non-Associative Day in
Online\n\n\nAbstract\nGiven an algebra $\\mathcal{A}$\, the polynomial in
variants $I_m(\\mathcal{A})$ of $m$-copies of $\\mathcal{A}$ with respect
to the action of the automorphism group of $\\mathcal{A}$ is a classical t
opic dating back to the 1970s\, beginning with works of Procesi and Sibirs
kii and later extended by Iltyakov. Recently\, generators for $I_m(\\mathc
al{A})$ were described for arbitrary two-dimensional algebras (Alvarez and
Lopatin\, 2025) and for arbitrary three-dimensional non-Lie Leibniz algeb
ras (Kaygorodov and Lopatin) over the complex numbers. We continue this li
ne of research by describing generators for $I_m(\\mathcal{A})$ when $\\ma
thcal{A}$ is a three-dimensional simple evolution algebra.\n
LOCATION:https://stable.researchseminars.org/talk/NonAssociativeDay/36/
END:VEVENT
END:VCALENDAR