BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Albert Schwarz (UC Davis)
DTSTART:20200827T170000Z
DTEND:20200827T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/1
DESCRIPTION:Title: Some questions on Jordan algebras inspired by quantum theory
\nby Albert Schwarz (UC Davis) as part of LieJor Online Seminar: Algeb
ras\, representations\, and applications\n\n\nAbstract\nOne can formulate
quantum theory taking as a starting point a convex set (the set of states)
or a convex cone (the set of non-normalized states.) Jordan algebras are
closely related to homogeneous cones\, therefore they appear naturally in
this formulation. There exists a conjecture that superstring can be formul
ated in terms of exceptional Jordan algebras. In my purely mathematical ta
lk I'll formulate some results and conjectures on Jordan algebras coming f
rom these ideas.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Mostovoy (SINVESTAV)
DTSTART:20200903T170000Z
DTEND:20200903T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/2
DESCRIPTION:Title: The Chevalley-Eilenberg complex for Leibniz and for Sabinin
algebras\nby Jacob Mostovoy (SINVESTAV) as part of LieJor Online Semin
ar: Algebras\, representations\, and applications\n\n\nAbstract\nI will sh
ow how to generalize the Chevalley-Eilenberg complex of a Lie algebra to S
abinin algebras and to Leibniz algebras. I will also show how Leibniz alge
bras can be interpreted as a very basic kind of DG Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20200910T170000Z
DTEND:20200910T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/3
DESCRIPTION:Title: The singular support of the Ising model\nby Reimundo Hel
uani (IMPA) as part of LieJor Online Seminar: Algebras\, representations\,
and applications\n\n\nAbstract\nWe prove three new q-series identities of
the Rogers-Ramanujan-Slater type. We find a PBW basis for the Ising model
as a consequence of one of these identities. If time permits it will be s
hown that the singular support of the Ising model is a hyper-surface (in t
he differential sense) on the arc space of it's associated scheme. This is
joint work with G. E. Andrews and J. van Ekeren and is available online a
t https://arxiv.org/abs/2005.10769\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Makar-Limanov (Wayne State University)
DTSTART:20200917T170000Z
DTEND:20200917T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/4
DESCRIPTION:by Leonid Makar-Limanov (Wayne State University) as part of Li
eJor Online Seminar: Algebras\, representations\, and applications\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Molev (University of Sidney)
DTSTART:20201001T130000Z
DTEND:20201001T140000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/5
DESCRIPTION:Title: Symmetrization map\, Casimir elements and Sugawara operators
\nby Alexander Molev (University of Sidney) as part of LieJor Online S
eminar: Algebras\, representations\, and applications\n\n\nAbstract\nThe c
anonical symmetrization map is a g-module isomorphism between the symmetri
c algebra S(g) of a finite-dimensional Lie algebra g and its universal env
eloping algebra U(g). This implies that the images of g-invariants in S(g)
are Casimir elements. For each simple Lie algebra g of classical type we
consider basic g-invariants arising from the characteristic polynomial of
the matrix of generators. We calculate the Harish-Chandra images of the co
rresponding Casimir elements. By using counterparts of the symmetric algeb
ra invariants for the associated affine Kac-Moody algebras we obtain new f
ormulas for generators of the centers of the affine vertex algebras at the
critical level. Their Harish-Chandra images are elements of classical W-a
lgebras which we produce in an explicit form.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Elduque (Universidad de Zaragoza)
DTSTART:20201008T170000Z
DTEND:20201008T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/6
DESCRIPTION:Title: Graded-simple algebras and twisted loop algebras\nby Alb
erto Elduque (Universidad de Zaragoza) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nThe loop algeb
ra construction by Allison\, Berman\, Faulkner\, and Pianzola (2008)\, des
cribes graded-central-simple algebras with "split centroid" in terms of ce
ntral simple algebras graded by a quotient of the original grading group.
Particular versions of this result were considered by several authors.\n\n
In this talk it will be shown how the restriction on the centroid can be r
emoved\, at the expense of allowing some deformations (cocycle twists) of
the loop algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Grantcharov (University of Texas Arlington)
DTSTART:20201015T170000Z
DTEND:20201015T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/7
DESCRIPTION:Title: Quantized enveloping superalgebra of type P\nby Dimitar
Grantcharov (University of Texas Arlington) as part of LieJor Online Semin
ar: Algebras\, representations\, and applications\n\n\nAbstract\nWe will i
ntroduce a new quantized enveloping superalgebra corresponding to the peri
plectic Lie superalgebra p(n). This quantized enveloping superalgebra is a
quantization of a Lie bisuperalgebra structure on p(n). Furthermore\, we
will define the periplectic q-Brauer algebra and see that it admits natura
l centralizer properties. This is joint work with N. Guay and S. Ahmed.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Kharlampovich (Hunter College CUNY)
DTSTART:20201029T170000Z
DTEND:20201029T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/8
DESCRIPTION:Title: Frasse limits of limit groups\nby Olga Kharlampovich (Hu
nter College CUNY) as part of LieJor Online Seminar: Algebras\, representa
tions\, and applications\n\n\nAbstract\nWe modify the notion of a Fraïss
é class and show that various interesting classes of groups\, notably the
class of nonabelian limit groups and the class of finitely generated elem
entary free groups\, admit Fraïssé limits. We will also discuss countabl
e elementary free groups. The talk is based on joint results with A. Miasn
ikov\, C. Natoli and R. Sklinos.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Mikhalev (Lomonosov Moscow State University)
DTSTART:20201112T160000Z
DTEND:20201112T170000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/9
DESCRIPTION:by A.V. Mikhalev (Lomonosov Moscow State University) as part o
f LieJor Online Seminar: Algebras\, representations\, and applications\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Bulgarian Academy of Sciences)
DTSTART:20201217T170000Z
DTEND:20201217T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/10
DESCRIPTION:Title: From a Diophantine transport problem from 2016 and its poss
ible solution from 1903 to classical problems in algebra\nby Vesselin
Drensky (Bulgarian Academy of Sciences) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nMotivated by
a recent Diophantine transport problem about how to transport profitably a
group of persons or objects\, we survey classical facts about solving sys
tems of linear Diophantine equations and inequalities in nonnegative integ
ers. We emphasize on the method of Elliott from 1903 and its further devel
opment by MacMahon in his “$\\Omega$-Calculus” or Partition Analysis.
Then we show how this approach can be used to solve problems in classical
and noncommutative invariant theory and theory of algebras with polynomial
identities. The obtained results are due to a big team of mathematicians
in Bulgaria\, Italy\, Turkey and Hungary. The talk is a joint project with
Silvia Boumova.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Louisiana State University)
DTSTART:20201001T150000Z
DTEND:20201001T160000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/11
DESCRIPTION:Title: Quantum cluster algebras at roots of unity and discriminant
s\nby Milen Yakimov (Louisiana State University) as part of LieJor Onl
ine Seminar: Algebras\, representations\, and applications\n\n\nAbstract\n
Cluster Algebra were invented by Fomin and Zelevinsky twenty years ago. Si
nce then they have played an important role in a number of settings in com
binatorics\, geometry\, representation theory and topology. We will introd
uce a notion of root of unity quantum cluster algebras which are PI algebr
as\, and will show that they have large canonical central subalgebras isom
orphic to the original cluster algebras. These are far reaching generaliza
tions of the De Concini-Kac-Procesi central subalgebras that appear in the
study of the irreducible representations of big quantum groups. We will d
escribe a general theorem computing the discriminants of these algebras. I
n a special situation it yields a formula for the discriminants of the qua
ntum unipotent cells at roots of unity associated to all symmetrizable Kac
-Moody algebras. This is a joint work with Bach Nguyen (Xavier Univ) and K
urt Trampel (Univ Notre Dame).\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Premet (University of Manchester)
DTSTART:20200924T170000Z
DTEND:20200924T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/12
DESCRIPTION:Title: Modular representations of Lie algebras and Humphreys' Conj
ecture\nby Alexander Premet (University of Manchester) as part of LieJ
or Online Seminar: Algebras\, representations\, and applications\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Libedinsky (Universidad de Chile)
DTSTART:20201105T170000Z
DTEND:20201105T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/13
DESCRIPTION:Title: On Kazhdan-Lusztig theory for affine Weyl groups\nby Ni
colas Libedinsky (Universidad de Chile) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nKazhdan-Luszt
ig polynomials are a big mystery. On a recent work with Leonardo Patimo (f
ollowing Geordie Williamson) we were able to calculate them explicitly for
affine A2. We dream of a similar description for all affine Weyl groups\,
but it seems like an incredibly difficult program. I will explain some ne
w results in this direction and what we believe that is doable. Another pa
rt of this project is to produce an approach towards the following questio
n: for a given element in an affine Weyl group\, what are the prime number
s p such that the p-canonical basis is different from the canonical basis?
This is a joint project with Leonardo Patimo and David Plaza.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claude Cibils (Université de Montpellier)
DTSTART:20201210T170000Z
DTEND:20201210T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/14
DESCRIPTION:Title: Controlling the global dimension\nby Claude Cibils (Uni
versité de Montpellier) as part of LieJor Online Seminar: Algebras\, repr
esentations\, and applications\n\n\nAbstract\nThe global dimension of an a
ssociative algebra A over a a field is a measure of the complexity of its
representations. It is 0 if A is a matrix algebra. It is 1 if A is a path
algebras of quivers without directed cycles. It is infinite if A is the al
gebra of dual numbers.\n\nI will give a brief introduction to Hochschild h
omology (1945)\, in order to explain Han's conjecture (2006): for finite-d
imensional algebras\, the Hochschild homology should control the finitenes
s of the global dimension.\n\nNext\, I will present some progress made in
showing the Han's conjecture\, using the relative version of Hochschild ho
mology (1956) with respect to a subalgebra B. This theory was little used
until recently. Now we have a Jacobi-Zariski long nearly exact sequence wh
ich relates the usual and relative versions of Hochschild homology. Its ga
p to be exact is approximated by a spectral sequence which has Tor functor
s in its first page\, of B-tensor powers of A/B. This tool enables to show
\, for instance\, that the class of algebras verifying Han's conjecture is
closed by bounded extensions of algebras. These results have been obtaine
d in joint work with M. Lanzilotta\, E. N. Marcos and A. Solotar.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Nakano (University of Georgia)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/15
DESCRIPTION:Title: A new Lie theory for classical Lie superalgebras\nby Da
niel Nakano (University of Georgia) as part of LieJor Online Seminar: Alge
bras\, representations\, and applications\n\n\nAbstract\nIn 1977\, Kac cla
ssified simple Lie superalgebras over \\({\\mathbb C}\\) and showed they p
lay an analogous role to simple Lie algebras over the complex numbers. For
simple algebraic groups and their Lie algebras\, the notions of a maximal
torus\, Borel subgroups and the Weyl groups provide a uniform method to t
reat the structure and representation theory for these groups and Lie alge
bras. Historically\, much of the work for simple Lie superalgebras has inv
olved dealing with these objects using a case by case analysis.
F
ifteen years ago\, Boe\, Kujawa and the speaker introduced the concept of
detecting subalgebras for classical Lie superalgebras. These algebras were
constructed by using ideas from geometric invariant theory. More recently
\, D. Grantcharov\, N. Grantcharov\, Wu and the speaker introduced the con
cept of a BBW parabolic subalgebra. Given a Lie superalgebra \\({\\mathfra
k g}\\)\, one has a triangular decomposition \\({\\mathfrak g}={\\mathfrak
n}^{-}\\oplus {\\mathfrak f} \\oplus {\\mathfrak n}^{+}\\) with \\({\\mat
hfrak b}={\\mathfrak f}\\oplus {\\mathfrak n}^{-}\\) where \\({\\mathfrak
f}\\) is a detecting subalgebra and \\({\\mathfrak b}\\) is a BBW paraboli
c subalgebra. This holds for all classical "simple" Lie superalgebras\, an
d one can view \\({\\mathfrak f}\\) as an analog of the maximal torus\, an
d \\({\\mathfrak b}\\) like a Borel subalgebra. This setting also provide
a useful method to define semisimple elements and nilpotent elements\, and
to compute various sheaf cohomology groups \\(R^{\\bullet}\\text{ind}_{B}
^{G} (-)\\).
The goal of my talk is to provide a survey of the m
ain ideas of this new theory and to give indications of the interconnectio
ns within the various parts of this topic. I will also indicate how this t
reatment can further unify the study of the representation theory of class
ical Lie superalgebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Zaicev (Lomonosov Moscow State University)
DTSTART:20201022T170000Z
DTEND:20201022T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/16
DESCRIPTION:Title: Polynomial identities: anomalies of codimension growth\
nby Mikhail Zaicev (Lomonosov Moscow State University) as part of LieJor O
nline Seminar: Algebras\, representations\, and applications\n\n\nAbstract
\nMikhail Zaicev (Lomonosov Moscow State University\, Russia): Polynomial
identities: anomalies of codimension growth. P
olynomial identities: anomalies of codimension growth.
Mikhail
Zaicev (Lomonosov Moscow State University\, Russia)
22/Oct/2020 - 14:00
GMT-3 (Sã\;o Paulo time)
We consider numerical invariants a
ssociated with polynomial identities of algebras over a field of character
istic zero. Given an algebra \\(A\\)\, one can construct a sequence of non
-negative integers \\({c_n(A)}\, n=1\,2\, \\ldots \\)\, called the codimen
sions of \\(A\\)\, which is an important numerical characteristic of ident
ical relations of \\(A\\). In present talk we discuss asymptotic behavior
of codimension sequence in different classes of algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Iyudu (University of Edinburgh)
DTSTART:20201119T170000Z
DTEND:20201119T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/17
DESCRIPTION:Title: On the proof of the Kontsevich conjecture on noncommutative
birational transformations\nby Natalia Iyudu (University of Edinburgh
) as part of LieJor Online Seminar: Algebras\, representations\, and appli
cations\n\n\nAbstract\nI will talk about our proof (arxiv 1305.1965\, Duke
math J.) of the Kontsevich conjecture (1996) on noncommutative birational
transformations. It deals with difficulties arising out of the fact that
there are no canonical form for noncommutative rational expressions. Mirac
ulous identities proved supposedly reflect some kind of noncommutative gro
up actions.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eli Aljadeff (Technion-Israel Institute of Technology)
DTSTART:20201126T170000Z
DTEND:20201126T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/18
DESCRIPTION:Title: PI theory\, generic objects and group gradings\nby Eli
Aljadeff (Technion-Israel Institute of Technology) as part of LieJor Onlin
e Seminar: Algebras\, representations\, and applications\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agata Smoktunowicz (University of Edinburgh)
DTSTART:20210225T170000Z
DTEND:20210225T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/19
DESCRIPTION:Title: Some questions related to nilpotent rings and braces\nb
y Agata Smoktunowicz (University of Edinburgh) as part of LieJor Online Se
minar: Algebras\, representations\, and applications\n\n\nAbstract\nIn aro
und 2005\, Wolfgang Rump introduced braces\, a generalisation of nilpotent
rings to describe all involutive\, non-degenerate set theoretic solutions
of the Yang-Baxter equation. This formulation then rapidly found applicat
ion in other research areas. This talk will review these applications.
Definition. A set \\(A\\) with binary operations of additio
n \\(+\\)\, and multiplication \\(\\circ\\) is a brace if \\((A\, +)\\) is
an abelian group\, \\((A\, \\circ)\\) is a group and \\(a \\circ (b+c) +a
= a \\circ b+a \\circ c\\) for every \\(a\, b\, c \\in A\\). It follows f
rom this definition that every nilpotent ring with the usual addition and
with multiplication \\(a \\circ b = ab + a + b\\) is a brace.
B
races have been shown to be equivalent to several concepts in group theory
such as groups with bijective 1-cocycles and regular subgroups of the hol
omorph of abelian groups. In algebraic number theory there is a correspond
ence between braces and Hopf-Galois extensions of abelian type first obser
ved by David Bachiller. There is also connection between R-braces and pre-
Lie algebras discovered by Wolfgang Rump in 2014. One generator braces hav
e been shown to describe indecomposable\, involutive solutions of the Yang
-Baxter equation.
On the other hand\, Anastasia Doikou and Robe
rt Weston have recently discovered some fascinating connections between br
aces and quantum integrable systems. In particular\, to find solutions of
the set-theoretic reflection equation it is needed to solve problems on so
me polynomial identities in nilpotent rings. Because previously the theory
of polynomial identities was mainly developed for prime rings\, and for t
he reflection equation we only consider nilpotent rings\, there are no kno
wn methods for solving such problems. We will mention some open problems o
n polynomial identities in nilpotent rings which appear in this situation.
\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (Université de Strasbourg)
DTSTART:20210304T170000Z
DTEND:20210304T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/20
DESCRIPTION:Title: Diamond Lemma and the Maurer-Cartan equation\nby Vladim
ir Dotsenko (Université de Strasbourg) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nI shall outli
ne a new approach to the Composition-Diamond Lemma for rewriting systems /
Gröbner-Shirshov bases; more specifically\, I shall explain how th
e Maurer-Cartan equation in the tangent complex of a monomial algebra lead
s to many different versions of the Composition-Diamond Lemma\, one for ea
ch representative of the tangent complex arising from a multigraded resolu
tion of such algebra. This is joint work with Pedro Tamaroff.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandr Zubkov (UAEU (United Arab Emirates))
DTSTART:20210311T170000Z
DTEND:20210311T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/21
DESCRIPTION:Title: Harish-Chandra pairs and group superschemes\nby Alexand
r Zubkov (UAEU (United Arab Emirates)) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nThe purpose of
my talk is to discuss the following results recently obtained in collabor
ation with A.Masuoka (Tsukuba University\, Japan). First\, we prove that a
certain category of Harish-Chandra pairs is equivalent to the category of
(not necessary affine) locally algebraic group superschemes. Using this f
undamental equivalence we superize the famous Barsotti-Chevalley theorem a
nd prove that the sheaf quotient of an algebraic group superscheme over it
s group super-subscheme is again a superscheme of finite type. I will also
formulate some open problems whose solving would bring significant progre
ss in the supergroup theory.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (The Weizmann Institute of Science\, Israel)
DTSTART:20210318T170000Z
DTEND:20210318T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/22
DESCRIPTION:Title: Depths and cores in the light of DS-functors\nby Maria
Gorelik (The Weizmann Institute of Science\, Israel) as part of LieJor Onl
ine Seminar: Algebras\, representations\, and applications\n\n\nAbstract\n
The Dulfo-Serganova functors DS are tensor functors relating representatio
ns of different Lie superalgebras. In this talk I will consider the behavi
our of various invariants\, such as the defect\, the dual Coxeter number\,
the atypicality and the cores\, under the DS-functor. I will introduce a
notion of depth playing the role of defect for algebras and atypicality fo
r modules. I will mainly concentrate on examples of symmetrizable Kac-Mood
y and Q-type superalgebras. The talk is based on arXiv:2010.05721\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apoorva Khare (Indian Institute of Science)
DTSTART:20210325T170000Z
DTEND:20210325T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/23
DESCRIPTION:Title: Polymath14: Groups with norms\nby Apoorva Khare (Indian
Institute of Science) as part of LieJor Online Seminar: Algebras\, repres
entations\, and applications\n\n\nAbstract\nConsider the following three p
roperties of a general group \\(G\\):
Algebra: \\(G\\) is abeli
an and torsion-free.
Analysis: \\(G\\) is a metric space that admits
a "norm"\, namely\, a translation-invariant metric \\(d(.\,.)\\) satisfyi
ng: \\(d(1\,g^n) = |n| d(1\,g)\\) for all \\(g \\in G\\) and integers \\(n
\\).
Geometry: \\(G\\) admits a length function with "saturated" sub
additivity for equal arguments: \\(l(g^2) = 2 l(g)\\) for all \\(g \\in G\
\).
While these properties may a priori seem different\, in fact
they turn out to be equivalent (and also to \\(G\\) being isometrically a
nd additively embedded in a Banach space\, hence inheriting its norm). The
nontrivial implication amounts to saying that there does not exist a non-
abelian group with a "norm". We will discuss motivations from analysis\, p
robability\, and geometry; then the proof of the above equivalences;
and finally\, the logistics of how the problem was solved\, via a PolyMat
h project that began on a blog post of Terence Tao.
(Joint - a
s D.H.J. PolyMath - with Tobias Fritz\, Siddhartha Gadgil\, Pace Nielsen\,
Lior Silberman\, and Terence Tao.)\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kang Seok-Jin (Korea Research Institute of Arts and Mathematics\,
South Korea)
DTSTART:20210401T130000Z
DTEND:20210401T140000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/24
DESCRIPTION:Title: Quantum Borcherds-Bozec algebras and abstract crystals\
nby Kang Seok-Jin (Korea Research Institute of Arts and Mathematics\, Sout
h Korea) as part of LieJor Online Seminar: Algebras\, representations\, an
d applications\n\n\nAbstract\nIn this talk\, we will discuss the basic pro
perties of quantum Borcherds-Bozec algebras and their integrable represent
ations. We also give a brief description of the theory of abstract crystal
s for quantum Borcherds-Bozec algebras and their applications.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Mukhin (IUPUI School of Science\, USA)
DTSTART:20210408T170000Z
DTEND:20210408T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/25
DESCRIPTION:Title: Supersymmetric analogs of partitions and plane partitions\nby Evgeny Mukhin (IUPUI School of Science\, USA) as part of LieJor Onl
ine Seminar: Algebras\, representations\, and applications\n\n\nAbstract\n
We will explain combinatorics of various partitions arising in the represe
ntation theory of quantum toroidal algebras associated to Lie superalgebra
gl(m|n). Apart from being interesting in its own right\, this combinatori
cs is expected to be related to crystal bases\, fixed points of the moduli
spaces of BPS states\, equivariant K-theory of moduli spaces of maps\, an
d other things. This talk is based on a joint project with Luan Bezerra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José María Pérez Izquierdo (Universidad de La Ri
oja\, Spain)
DTSTART:20210415T170000Z
DTEND:20210415T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/26
DESCRIPTION:Title: Some aspects of the free nonassociative algebra\nby Jos
é María Pérez Izquierdo (Universidad de La Rioja\, Spain
) as part of LieJor Online Seminar: Algebras\, representations\, and appli
cations\n\n\nAbstract\nThe free nonassociative algebra provides a simple c
ombinatorial context to extend some constructions from the associative set
ting. In this talk\, based on joint work with J. Mostovoy and I. P. Shesta
kov\, I will briefly discuss three of them related to nonassociative Lie t
heory: the embedding of the free loop as nonassociative formal power serie
s\, a nonassociative extension of the Baker-Campbell-Hausdorff formula and
a nonassociative version of Solomon's descent algebra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Belolipetsky (IMPA\, Brazil)
DTSTART:20210422T180000Z
DTEND:20210422T190000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/27
DESCRIPTION:Title: Growth of lattices in semisimple Lie groups\nby Mikhail
Belolipetsky (IMPA\, Brazil) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nA discrete subgroup \\(
G\\) of a Lie group \\(H\\) is called a lattice if the quotient space \\(H
/G\\) has finite volume. By a classical theorem of Bieberbach we know that
the group of isometries of an \\(n\\)-dimensional Euclidean space has onl
y finitely many different types of lattices. The situation is different fo
r the semisimple Lie groups \\(H\\). Here the total number of lattices is
infinite and we can study its growth rate with respect to the covolume. Th
is topic has been a subject of our joint work with A. Lubotzky for a numbe
r of years. In the talk I will discuss our work and some other more recent
related results.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Shpectorov (University of Birmingham\, UK)
DTSTART:20210429T170000Z
DTEND:20210429T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/28
DESCRIPTION:Title: 2-generated algebras of Monster type\nby Sergey Shpecto
rov (University of Birmingham\, UK) as part of LieJor Online Seminar: Alge
bras\, representations\, and applications\n\n\nAbstract\nThe class of non-
associative axial algebras was introduced in 2015 as a broad generalisatio
n of Majorana algebras of Ivanov that were modelled after the properties o
f the Griess algebra\, the algebra whose automorphism group is the Monster
sporadic simple group. Sakuma's theorem classifies 2-generated Majorana a
lgebras\, which in axial terms correspond to algebras of Monster type (1/4
\,1/32). The quest to classify all 2-generated algebras of arbitrary Monst
er type \\((\\alpha\,\\beta)\\) was started by Rehren who proved an upper
bound on the dimension and generalised the Norton-Sakuma algebras to arbit
rary \\((\\alpha\,\\beta)\\). Recently\, new results emerged from the work
of Franchi\, Mainardis and the speaker\, and independently\, of Yabe\, wh
o classified symmetric 2-generated algebras of Monster type. Several new c
lasses of algebras have been found.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Rozhkovskaya (Kansas State University\, USA)
DTSTART:20210506T170000Z
DTEND:20210506T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/29
DESCRIPTION:Title: Generating functions of polynomial tau-functions of the sol
iton hierarchies\nby Natasha Rozhkovskaya (Kansas State University\, U
SA) as part of LieJor Online Seminar: Algebras\, representations\, and app
lications\n\n\nAbstract\nThe Kademtsev-Petviashvily (KP) equation is a fam
ous evolution equation with soliton solutions. It was discovered by M.Sato
and the Kyoto school that the KP equation can be regarded as a part of a
countable system of compatible evolution equations\, which is called today
the KP hierarchy. The observation allowed the researchers to discover man
y new examples of soliton type hierarchies and to study them with methods
of mathematical physics\, algebraic geometry and representation theory. In
the talk we will describe the explicit construction of polynomial tau-fun
ctions of the KP\, BKP hierarchies through their generating functions. The
method uses the tools of representation theory and properties of symmetri
c functions. The talk is based on the joint work with V. G. Kac and J. van
de Leur.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa\, Canada)
DTSTART:20210513T170000Z
DTEND:20210513T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/30
DESCRIPTION:Title: Affine Hecke algebras and the elliptic Hall algebra\nby
Alistair Savage (University of Ottawa\, Canada) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nThe
elliptic Hall algebra has appeared in many different contexts in represent
ation theory and geometry under different names. We will explain how this
algebra is categorified by the quantum Heisenberg category\, which is a di
agrammatic category modelled on affine Hecke algebras. This categorificati
on can be used to construct large families of representations for the elli
ptic Hall algebra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farkhod Eshmatov (Academy of Science of Uzbekistan\, Uzbekistan)
DTSTART:20210520T170000Z
DTEND:20210520T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/31
DESCRIPTION:Title: On transitive action on quiver varieties\nby Farkhod Es
hmatov (Academy of Science of Uzbekistan\, Uzbekistan) as part of LieJor O
nline Seminar: Algebras\, representations\, and applications\n\n\nAbstract
\nThe Calogero-Moser space \\({\\mathcal C}_n\\) is the space of conjugacy
classes of pairs of \\(n \\times n\\) matrices such that the matrix \\(XY
- Y X + I_n\\) has rank one. These spaces play important role in geometry
\, representation theory and integrable systems. A well-known result of Be
rest and Wilson states that the natural action of the affine Cremona group
\\(GA_2\\) on \\({\\mathcal C}_n\\) is transitive. In this talk we will g
ive a quiver generalization of this statement and discuss some application
s.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kleshchev (University of Oregon\, USA)
DTSTART:20210527T170000Z
DTEND:20210527T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/32
DESCRIPTION:Title: Irreducible restrictions from symmetric groups to subgroups
\nby Alexander Kleshchev (University of Oregon\, USA) as part of LieJo
r Online Seminar: Algebras\, representations\, and applications\n\n\nAbstr
act\nWe motivate\, discuss history of\, and present a solution to the foll
owing problem: describe pairs \\((G\,V)\\) where \\(V\\) is an irreducible
representation of the symmetric group \\(S_n\\) of dimension \\(>1\\) and
\\(G\\) is a subgroup of \\(S_n\\) such that the restriction of \\(V\\) t
o \\(G\\) is irreducible. We do the same with the alternating group \\(A_n
\\) in place of \\(S_n\\). The latest results on the problem are joint wit
h Pham Huu Tiep and Lucia Morotti.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Bavula (The University of Sheffield\, UK)
DTSTART:20210401T170000Z
DTEND:20210401T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/33
DESCRIPTION:Title: The global dimension of the algebras of polynomial integro-
differential operators and the Jacobian algebras\nby Vladimir Bavula (
The University of Sheffield\, UK) as part of LieJor Online Seminar: Algebr
as\, representations\, and applications\n\n\nAbstract\nWe review some old
and recent results about the algebras of polynomial integro-differential o
perators and the Jacobian algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shavkat Ayupov (V.I.Romanovskiy Institute of Mathematics Uzbekista
n Academy of Sciences)
DTSTART:20210415T150000Z
DTEND:20210415T160000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/34
DESCRIPTION:Title: Local and 2-local derivations and automorphisms of Octonian
algebras\nby Shavkat Ayupov (V.I.Romanovskiy Institute of Mathematics
Uzbekistan Academy of Sciences) as part of LieJor Online Seminar: Algebra
s\, representations\, and applications\n\n\nAbstract\nThe talk is devoted
to description of local and 2-local derivations (respectively\, automorphi
sms) on octonian algebras over fields with zero characteristics. We shall
give a general form of local derivations on the real octonion algebra \\(O
(\\mathbb{R})\\). This description implies that the space of all local der
ivations on \\(O(\\mathbb{R})\\) when equipped with Lie bracket is isomorp
hic to the Lie algebra \\(so_7(\\mathbb{R})\\) of all real skew-symmetric
\\(7 \\times 7\\)-matrices. We also consider 2-local derivations on the oc
tonion algebra \\(O(F)\\) over an algebraically closed field \\(F\\) and p
rove that every 2-local derivation on \\(O(F)\\) is a derivation. Further\
, we apply these results to problems for the simple 7-dimensional Malcev a
lgebra. As a corollary we obtain that the real octonion algebra \\(O(\\mat
hbb{R})\\) and Malcev algebra \\(M_7(R)\\) are simple non associative alge
bras which admit pure local derivations\, that is\, local derivations whic
h are not derivation. Further\, we shall give a general form of local auto
morphisms on the octonion algebra \\(O(F)\\) over a field \\(F\\). This de
scription implies that the group of all local automorphisms on \\(O(F)\\)
is isomorphic to the group \\(O_7(F)\\) of all orthogonal \\(7 \\times 7\\
)-matrices over F. We also consider 2-local automorphisms on the octonion
algebra \\(O(F)\\) over an algebraically closed field \\(F\\) and prove th
at every 2-local automorphism on \\(O(F)\\) is an automorphism. As a corol
lary we obtain descriptions of local and 2-local automorphisms of seven di
mensional simple Malcev algebra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (IME-USP\, Brazil)
DTSTART:20210603T170000Z
DTEND:20210603T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/35
DESCRIPTION:Title: Infinite-dimensional representations of Lie algebras\nb
y Vyacheslav Futorny (IME-USP\, Brazil) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nWe will discu
ss the representation theory of simple finite-dimensional Lie algebras\,
Affine Lie algebras and their generalizations. Special focus will be given
to the representations of vertex algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Pantev (University of Pennsylvania\, USA)
DTSTART:20210610T170000Z
DTEND:20210610T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/36
DESCRIPTION:Title: Geometry and topology of wild character varieties\nby T
ony Pantev (University of Pennsylvania\, USA) as part of LieJor Online Sem
inar: Algebras\, representations\, and applications\n\n\nAbstract\nWild ch
aracter varieties parametrize monodromy representations of flat meromorphi
c connections on compact Riemann surfaces. They are classical objects with
remarkable geometric and topological properties. \n\nI will recall how in
trinsic geometric structures resolve singularities of wild character varie
ties and will show that known algebraic symplectic structures extend natur
ally to the resolutions. This is based on a new universal method for produ
cing symplectic structures which is a joint work with Arinkin and Toen. Ti
me permitting I may also describe recent joint works with Chuang\, Diacone
scu\, Donagi\, and Nawata which extract cohomological invariants of wild c
haracter varieties from enumerative Calabi-Yau geometry and refined Chern-
Simons invariants of torus knots.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geordie Williamson (University of Sydney\, Australia)
DTSTART:20210617T200000Z
DTEND:20210617T210000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/37
DESCRIPTION:Title: Spectra in representation theory\nby Geordie Williamson
(University of Sydney\, Australia) as part of LieJor Online Seminar: Alge
bras\, representations\, and applications\n\n\nAbstract\nIn geometric repr
esentation theory cohomology\, intersection cohomology and constructible s
heaves show up everywhere. This might seem strange to an algebraic topolog
ist\, who might ask: why this emphasis on cohomology\, when there are so m
any other interesting cohomology theories (like K-theory\, elliptic cohomo
logy\, complex cobordism\, ...) out there? They might also ask: is there s
omething like "intersection K-theory"\, or "intersection complex cobordism
"? This is something I've often wondered about. I will describe work in pr
ogress with Ben Elias\, where we use Soergel bimodules to investigate what
KU-modules look like on the affine Grassmannian. We have checked by hand
that in types A1\, A2 and B2\, one gets something roughly resembling the q
uantum group. Speaking very roughly\, the intersection K-theory of Schuber
t varieties in the affine Grassmannian should recover the irreducible repr
esentations of the quantum group. Inspirations for this work include a str
ange Cartan matrix discovered by Ben Elias\, and work of Cautis-Kamnitzer.
\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitaly A. Roman'kov (Sobolev Institute of Mathematics RAS\, Omsk B
ranch\, Omsk\, Russia)
DTSTART:20210624T170000Z
DTEND:20210624T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/38
DESCRIPTION:Title: Embedding theorems for solvable groups\nby Vitaly A. Ro
man'kov (Sobolev Institute of Mathematics RAS\, Omsk Branch\, Omsk\, Russi
a) as part of LieJor Online Seminar: Algebras\, representations\, and appl
ications\n\n\nAbstract\nIn this talk\, we present a series of results on g
roup embeddings in groups with a small number of generators. We show that
each finitely generated group \\(G\\) lying in a variety M can be embedded
in a 4-generated group \\(H\\) in a variety MA\, where a A means the var
iety of abelian groups. If \\(G\\) is a finite group\, then \\(H\\) can al
so be found as a finite group. It follows\, that any finitely generated (f
inite) solvable group \\(G\\) of the derived length \\(l\\) can be embedde
d in a 4-generated (finite) solvable group \\(H\\) of length \\(l+1\\). Th
us\, we answer the question of V. H. Mikaelian and A.Yu. Olshanskii. It is
also shown that any countable group \\(G\\) in M\, such that the abeliani
zation \\(G_{ab}\\) is a free abelian group\, is embeddable in a 2-generat
ed group \\(H\\) in MA.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry V. Artamonov (Lomonosov State University\, Moscow)
DTSTART:20210701T170000Z
DTEND:20210701T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/39
DESCRIPTION:Title: \\(3j\\)-symbols for the algebra \\(gl_3\\)\nby Dmitry
V. Artamonov (Lomonosov State University\, Moscow) as part of LieJor Onlin
e Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nTh
e problem of caculation of Clebsh-Gordan coefficients for a tensor product
of two irreducible representations of the Lie algebra \\(gl_2\\) is well-
investigated. It's solution plays an importan role in quantum mechanics. A
nalogous problem for the algebra \\(gl_3\\) is also improtant (in the theo
ry of quarks)\, but it it much l more difficult. In some sence it was solv
ed in the 60-s in a series of papers by Biedenharn\, Louck\, Baird. But
their solution is very cumbersome and not explicit. Thus the problem of f
indind of an explicit and simple formula for a Clebsh-Gordan coefficient r
emained unsolved.
In the talk an explicit and simple formula for
a Clebsh-Gordan coefficient for the algebra \\(gl_3\\) will be presented
. The answer will be given as a value at \\(1\\) of some \\(A\\)-hypergeom
etric function.
As a byproduct I shall give an explicit descripti
on of invariants in triple tensor product and a projection on the corres
ponding trivial representation.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kotchetov (Memorial University of Newfoundland\, Canada)
DTSTART:20210708T170000Z
DTEND:20210708T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/40
DESCRIPTION:Title: Fine gradings on classical simple Lie algebras\nby Mikh
ail Kotchetov (Memorial University of Newfoundland\, Canada) as part of Li
eJor Online Seminar: Algebras\, representations\, and applications\n\n\nAb
stract\nGradings by abelian groups have played an important role in the th
eory of Lie algebras since its beginning: the best known example is the ro
ot space decomposition of a semisimple complex Lie algebra\, which is a gr
ading by a free abelian group (the root lattice). Involutive automorphisms
or\, equivalently\, gradings by the cyclic group of order 2\, appear in t
he classification of real forms of these Lie algebras. Gradings by all cyc
lic groups were classified by V. Kac in the late 1960s and applied to the
study of symmetric spaces and affine Kac-Moody Lie algebras.\n\nIn the pas
t two decades there has been considerable interest in classifying gradings
by arbitrary groups on algebras of different varieties including associat
ive\, Lie and Jordan. Of particular importance are the so-called fine grad
ings (that is\, those that do not admit a proper refinement)\, because any
grading on a finite-dimensional algebra can be obtained from them via a g
roup homomorphism\, although not in a unique way. If the ground field is a
lgebraically closed and of characteristic 0\, then the classification of f
ine abelian group gradings on an algebra (up to equivalence) is the same a
s the classification of maximal quasitori in the algebraic group of automo
rphisms (up to conjugation). Such a classification is now known for all fi
nite-dimensional simple complex Lie algebras.\n\nIn this talk I will revie
w the above mentioned classification and present a recent joint work with
A. Elduque and A. Rodrigo-Escudero in which we classify fine gradings on c
lassical simple real Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Lubotzky (Hebrew University\, Jerusalem\, Israel)
DTSTART:20210715T170000Z
DTEND:20210715T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/41
DESCRIPTION:Title: First order rigidity of high-rank arithmetic groups\nby
Alex Lubotzky (Hebrew University\, Jerusalem\, Israel) as part of LieJor
Online Seminar: Algebras\, representations\, and applications\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Berest (Cornell University\, USA)
DTSTART:20210722T170000Z
DTEND:20210722T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/42
DESCRIPTION:Title: Spaces of quasi-invariants and homotopy Lie groups\nby
Yuri Berest (Cornell University\, USA) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nQuasi-invarian
ts are natural algebraic generalizations of classical invariant polynomial
s of finite reflection groups. They first appeared in mathematical physics
--- in the work of O. Chalykh and A. Veselov on quantum integrable system
s --- in the early 1990s\, and since then have found many interesting appl
ications in other areas: most notably\, representation theory\, algebraic
geometry and combinatorics.\n\nIn this talk\, I will explain how the algeb
ras of quasi-invariants arise in topology: as cohomology rings of certain
spaces naturally attached to compact connected Lie groups. Our main result
is a generalization of a well-known theorem of A. Borel that realizes the
algebra of classical invariant polynomials of a Weyl group W(G) as the co
homology ring of the classifying space BG of the corresponding Lie group G
. Perhaps most interesting here is the fact that our construction of space
s of quasi-invariants is purely homotopy-theoretic. It can therefore be ex
tended to some non-Coxeter (p-adic pseudo-reflection) groups\, in which ca
se the compact Lie groups are replaced by the so-called p-compact groups (
a.k.a. homotopy Lie groups).\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Onofrio Mario Di Vincenzo (Università di Basilicata\, Potenza\, I
taly)
DTSTART:20210729T170000Z
DTEND:20210729T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/43
DESCRIPTION:Title: Algebras and superalgebras with (super-)involutions and the
ir polynomial identities\nby Onofrio Mario Di Vincenzo (Università di
Basilicata\, Potenza\, Italy) as part of LieJor Online Seminar: Algebras\
, representations\, and applications\n\n\nAbstract\nIn this talk we consid
er the *-polynomial identities of algebras with involutions. The positive
solution of Specth's problem\, given by Aljadeff\, Giambruno and Karasik i
n [E. Aljadeff\, A. Giambruno\, Y. Karasik Polynomial identities with invo
lution\, super-involutions and the Grassmann envelope\, Proc. Amer. Math.
Soc. 145 (2017)\, no. 5\,1843-1857]\, for the T*-ideals of the free algebr
a with involution\, show the decisive role of the identities of finite dim
ensional superalgebras with superinvolution. In this talk we consider bloc
k-triangular matrix algebras related to any sequence of such *-simple supe
ralgebras. These *-simple superalgebras are also involved in determining t
he exact value of the correponding exponent as proved in [A. Ioppolo The e
xponent for superalgebras with superinvolution\, Linear Algebra and its Ap
plications Amer. Math. Soc. 555 (2018)\, 1-20]. We review the results in t
his area and we show that that every minimal affine variety of superalgebr
as with superinvolution is generated by one of the block triangular matrix
algebras we introduced\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kanel-Belov (Bar Ilan University\, Israel)
DTSTART:20210805T170000Z
DTEND:20210805T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/44
DESCRIPTION:Title: Evaluations of nonassociative polynomials on finite dimensi
onal algebras\nby Alexei Kanel-Belov (Bar Ilan University\, Israel) as
part of LieJor Online Seminar: Algebras\, representations\, and applicati
ons\n\n\nAbstract\nLet \\(p\\) be a polynomial in several non-commuting v
ariables with coefficients in an algebraically closed field \\(K\\) of arb
itrary characteristic. It has been conjectured that for any \\(n\\)\, for
\\(p\\) multilinear\, the image of \\(p\\) evaluated on the set \\(M_n(K)\
\) of \\(n\\) by \\(n\\) matrices is either zero\, or the set of scalar ma
trices\, or the set \\(sl_n(K)\\) of matrices of trace 0\, or all of \\(M_
n(K)\\).
In this talk we will discuss the generalization of this
result for non-associative algebras such as Cayley-Dickson algebra (i.e.
algebra of octonions)\, pure (scalar free) octonion Malcev algebra and bas
ic low rank Jordan algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Romanovskiy (Novosibirsk State University\, Russia)
DTSTART:20210812T150000Z
DTEND:20210812T160000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/45
DESCRIPTION:Title: Rigid solvable groups. Algebraic geometry and model theory<
/a>\nby Nikolay Romanovskiy (Novosibirsk State University\, Russia) as par
t of LieJor Online Seminar: Algebras\, representations\, and applications\
n\n\nAbstract\nA solvable group \\(G\\) is called rigid\, more precisely \
\(m\\)-rigid\, if there exists a normal series of subgroups \\(G=G_1 > G_2
> \\ldots > G_m > G_{m+1}=1\,\\) where all quotients \\(G_i/G_{i+1}\\) ar
e abelian and when viewed as right modules over \\(\\mathbb{Z} [G/G_i]\\)\
, do not have torsion. Free solvable groups and iterated wreath products o
f torsion free abelian groups are rigid\, as well as their subgroups. A ri
gid group \\(G\\) is termed divisible if elements of the quotient \\(G_i/G
_{i+1}\\) are divisible by non-zero elements of the ring \\(\\mathbb{Z} [G
/G_i]\\)\, i.e. \\(G_i/G_{i+1}\\) is a vector space over the skew-field of
fractions \\(Q(G/G_i)\\) of the ring \\(\\mathbb{Z} [G/G_i]\\) (such a sk
ew-field exists).
The talk will present the results of the author
and A. Myasnikov. Among them\, on the algebraic geometry of rigid groups\
, we state the main two: it is proved that any rigid group is equationally
Noetherian\, and the coordinate groups of irreducible algebraic sets over
a divisible rigid group are described. The theory of models of divisible
m-rigid groups is in many ways similar to the classical theory of models o
f algebraically closed fields. The axiomatics of the theory of divisible m
-rigid groups is found\, \\(\\omega\\)-stability is proved\, saturated mod
els are described\, the elimination of quantifiers is found\, the problems
of calculating the Morley rank are studied. Model theory results use alge
braic geometry over divisible rigid groups.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugeny Plotkin (Bar-Ilan University\, Israel)
DTSTART:20210819T170000Z
DTEND:20210819T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/46
DESCRIPTION:Title: Bounded generation and logical properties for linear and Ka
c-Moody cases\nby Eugeny Plotkin (Bar-Ilan University\, Israel) as par
t of LieJor Online Seminar: Algebras\, representations\, and applications\
n\n\nAbstract\nWe will survey a series of recent developments in the area
of bounded generation and first-order descriptions of groups. The goal is
to illuminate the known results relevant to logical characterizations of C
hevalley and Kac-Moody groups. If time permits I will discuss related ques
tions originated from universal algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Askar Dzhumadil'daev (Academy of Sciences of Kazakhstan\, Kazakhst
an)
DTSTART:20210826T170000Z
DTEND:20210826T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/47
DESCRIPTION:Title: Dimension formula for Koszul operads\nby Askar Dzhumadi
l'daev (Academy of Sciences of Kazakhstan\, Kazakhstan) as part of LieJor
Online Seminar: Algebras\, representations\, and applications\n\n\nAbstrac
t\nWe give recurrence formula for dimensions of Koszul operads. For exampl
e\, dimensions of multi-linear parts of Lie-admissible operad satisfy the
following recurrence relations \\(d_n=\\sum_{i=1}^{n-1}\\mu k B_{n-1\,k}(d
_1\,\\ldots\,d_{n-1})\,\\) where \\(B_{n\,k}\\) are Bell polynomial and \\
(\\mu_k=k!\\sum_{i=0}^k (k-i+1)^i/i!\\). If \\(p>3\\) is prime\, then \\(d
_{p-1}\\equiv 1 (mod p)\,\\) \\(d_{p}\\equiv -1(mod p)\,\\) \\(d_{p+1}\\eq
uiv -1(mod p)\,\\) \\(d_{p+2}\\equiv -6(mod p)\,\\) \\(d_{p+3}\\equiv -56
(mod p)\,\\) \\(d_{p+4}\\equiv -725(mod p).\\)\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitry Leites (New York University Abu Dhabi\, United Arab Emirat
es and Stockholm University\, Sweden)
DTSTART:20210902T170000Z
DTEND:20210902T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/48
DESCRIPTION:Title: Classifications of simple Lie (super)algebras and algebras
"more interesting" than simple\nby Dimitry Leites (New York University
Abu Dhabi\, United Arab Emirates and Stockholm University\, Sweden) as pa
rt of LieJor Online Seminar: Algebras\, representations\, and applications
\n\n\nAbstract\nI intend to overview classifications of simple Lie (super)
algebras of finite dimension and of polynomial growth. Various properties
of complex Lie superalgebras resemble same of modular Lie algebras. I will
encourage to consider these classifications without fanaticism: certain n
on-simple Lie (super)algebras\, "close" to simple ones\, are often "better
" for us than simple ones.\n\nInteresting features of deformations: semi-t
rivial deformations and (in super setting) odd parameters.\n\nI'll formula
te classification of finite-dimensional simple complex Lie superalgebras\,
odd parameters including.\n\nI'll formulate a definition of Lie superalge
bra suitable for any characteristic and classification of simple (finite-d
imensional) Lie superalgebras over algebraically closed fields of characte
ristic 2. With a catch: modulo (a) classification of simple (finite-dimens
ional) Lie superalgebras (over the same field) and (b) classification of t
heir gradings modulo 2. I'll mention conjectures on classification of modu
lar Lie algebras and superalgebras.\n\nIs it feasible to classify simple f
iltered Lie (super)algebras of polynomial growth? Interesting examples: de
forms of the Poisson Lie (super)algebras\, Lie (super)algebras of "matrice
s of complex size"\, etc.\n\nExamples. Double extensions of simple Lie (su
per)algebras are definitely "more interesting" than the simple objects the
y extend.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ofelia Ronco (Universidad de Talca\, Chile)
DTSTART:20210909T170000Z
DTEND:20210909T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/49
DESCRIPTION:Title: Generalization of dendriform algebras\nby Maria Ofelia
Ronco (Universidad de Talca\, Chile) as part of LieJor Online Seminar: Alg
ebras\, representations\, and applications\n\n\nAbstract\nIn a joint work
with D. López N. and L.-F. Préville-Ratelle [D. Lopez\, L.-F.
Préville-Ratelle\, M. Ronco\, Algebraic structures defined on \\(m\
\)-Dyck paths\, preprint arxiv:1508.01252 (2015)] we introduce a family of
non-symmetric operads \\({\\mbox{Dyck}^m}\\)\, which satisfies that:
1. \\({\\mbox{Dyck}^0}\\) is the operad of associative algebras\,
2. \\({\\mbox{Dyck}^1}\\) is the operad \\({\\mbox{Dend}}\\) of dendr
iform algebras\, introduced by J.-L. Loday in [J.-L. Loday\, Dialgebras\,
in Dialgebras and related operads\, Lecture Notes in Math.\, 1763\, Spring
er\, Berlin (2001) 7-66]\,
3. the vector space spanned by the set
of \\(m\\)-Dyck paths has a natural structure of free \\({\\mbox{Dyck}^m}\
\) algebra over one element\,
4. for any \\(k\\geq 1\\)\, there e
xist degeneracy operators \\(s_i: {\\mbox{Dyck}^m}\\longrightarrow {\\mbox
{Dyck}^{m-1}}\\) and face operators \\(d_j: {\\mbox{Dyck}^m}\\longrightar
row {\\mbox{Dyck}^{m+1}}\\)\, which defines a simplicial complex in the ca
tegory of non-symmetric operads.
The main examples of \\({\\mbox{D
yck}^m}\\) algebra are the vector spaces spanned by the \\(m\\)-simplices
of certain combinatorial Hopf algebras\, like the Malvenuto-Reutenauer alg
ebras and the algebra of packed words.
A well-known result on ass
ociative algebras states that\, as \\({\\mathcal S}\\)-module\, the operad
of \\({\\mbox{Ass}}\\) of associative algebras is the composition \\({\\
mbox{Ass}} ={\\mbox{Com}}\\circ {\\mbox{Lie}}\\)\, where \\({\\mbox{Com}}\
\) is the operad of commutative algebras and \\({\\mbox{Lie}}\\) is the op
erad of Lie algebras. The version of this result for dendriform algebras (
see [M. Ronco\, Eulerian idempotents and Milnor-Moore theorem for certain
non-cocommutative Hopf algebras\, J. of Algebra 254 (2002) 152-172.])\, is
that \\({\\mbox{Dend}} = {\\mbox{Ass}}\\circ {\\mbox{Brace}}\\)\, where \
\({\\mbox{Brace}}\\) is the operad of brace algebras\, defined in [M. Gers
tenhaber\, A. Voronov\, Homotopy G-algebras and moduli space operad\, Int
ernat. Math. Research Notices (1995)\, 141-153.] and [E. Getzler\, Cartan
homotopy formulas and the Gauss-Manin connection in cyclic homology\, Isra
el Math. Conf. Proc. 7 (1993)\, 65-78.].
Our goal is to introduce
the notion of \\(m\\)-brace algebra\, for \\(m\\geq 2\\)\, and prove that
there exists a Poincaré-Birkoff-Witt Theorem in this context\, stat
ing that \\({\\mbox{Dyck}^m} = {\\mbox{Ass}}\\circ {\\mbox{m-Brace}}\\). <
br>
Joint work with: Muriel Livernet\,Dept. of Mathématiques\, U
niv. de Paris-Diderot\, France.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Vojtechovsky (Denver University\, USA)
DTSTART:20210916T170000Z
DTEND:20210916T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/50
DESCRIPTION:Title: Quandles and other classes of set-theoretic solutions of th
e Yang-Baxter equation\nby Petr Vojtechovsky (Denver University\, USA)
as part of LieJor Online Seminar: Algebras\, representations\, and applic
ations\n\n\nAbstract\nQuandles are algebraic structures designed to mesh w
ith the Reidemeister moves of knot theory. Joyce and Matveev showed that q
uandles give rise to a complete invariant of oriented knots. Since the Yan
g-Baxter equation resembles the third Reidemeister move\, it is not surpri
sing that quandles also form a class of set-theoretic solutions of the Yan
g-Baxter equation. In this talk I will explain how quandles and connected
quandles can be enumerated up to isomorphism and list a few open problems.
I will also present two additional classes (involutive and idempotent) of
set-theoretic solutions of the Yang-Baxter equation with rich algebraic t
heory.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valery Bardakov (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20210923T170000Z
DTEND:20210923T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/51
DESCRIPTION:Title: Quandles and quandle rings\nby Valery Bardakov (Sobolev
Institute of Mathematics\, Novosibirsk\, Russia) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nAt
the first part of my talk I give a definition and examples of racks and qu
andles\, explain their connection with knot theory and with set-theoretic
solutions of the Yang-Baxter equation. Further I introduce some properties
of quandles: residually finiteness\, orderability\, and formulate results
on quandles which have these properties.\n\nThe second part of my talk is
dedicated to quandle rings. I introduce generalized quandle ring\, augmen
ted ideal\, describe relationships between subquandles of the given quandl
e and ideals of the associated quandle ring. The construction of the quoti
ent quandle leads to a correspondence between subquandles of the given qua
ndle and ideals of the quandle ring.\n\nI formulate some results on zero-d
ivisors in quandle rings. Some of these results answer a question of M. El
hamdadi\, N. Fernando and B. Tsvelikhovskiy [J. Algebra\, 526 (2019)\, 166
-187] on quandle rings which do not have zero-divisors.\n\nWe discuss a pr
oblem of the computation of idempotents in quandle rings. The computation
of idempotents is then used to determine automorphism groups of some quand
le rings.\n\nI introduce the commutator width of quandle rings and compute
the precise commutator width for some quandle rings.\n\nWe also discuss r
elations of quandle algebras with other well-known non-associative algebra
s like alternative algebras\, Jordan algebras and Lie algebras.\n\nAt the
end of the talk I formulate some open problems on quandle rings.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Semrl (University of Ljubljana\, Slovenia)
DTSTART:20210930T170000Z
DTEND:20210930T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/52
DESCRIPTION:Title: On Wigner's theorem\nby Peter Semrl (University of Ljub
ljana\, Slovenia) as part of LieJor Online Seminar: Algebras\, representat
ions\, and applications\n\n\nAbstract\nSome recent improvements of Wigner'
s unitary-antiunitary theorem will be presented. A connection with Gleason
's theorem will be explained.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael J. Larsen (Indiana University\, USA)
DTSTART:20211007T170000Z
DTEND:20211007T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/53
DESCRIPTION:Title: Quotients of normal subsets in simple groups\nby Michae
l J. Larsen (Indiana University\, USA) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nLet \\(G\\) be
a finite simple group and \\(S\\) a normal subset of \\(G\\). If \\(|G|\
\) is large enough in terms of \\(|S|/|G|\\)\, can we deduce that every el
ement of \\(G\\) can be expressed as \\(x y^{-1}\\) for \\(x\\) and \\(y\\
) elements of \\(S\\)? Shalev\, Tiep\, and I have proven that this is tru
e assuming \\(G\\) is an alternating group or a group of Lie type in bound
ed rank\, but the question remains open for classical groups of high rank
over small fields. I will say something about the methods of proof\, whic
h involve both character methods and geometric ideas and also say somethin
g about the more general question of covering \\(G\\) by \\(ST\\) where \\
(S\\) and \\(T\\) are large normal subsets.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Rowen (Bar-Ilan University\, Israel)
DTSTART:20211014T170000Z
DTEND:20211014T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/54
DESCRIPTION:Title: Finitely generated axial algebras\nby Louis Rowen (Bar-
Ilan University\, Israel) as part of LieJor Online Seminar: Algebras\, rep
resentations\, and applications\n\n\nAbstract\nThis lecture is a continuat
ion of the general talk given at the Drensky conference last month\, on ax
ial algebras\, which are (not necessarily commutative\, not necessarily as
sociative) algebras generated by semisimple idempotents. After a review of
the definitions\, we investigate the key question\, being\, "Under what c
onditions must an axial algebra be finite dimensional?" Krupnik showed tha
t 3 idempotents can generate arbitrarily large dimensional associative alg
ebras (and thus infinite dimensional algebras via an ultraproduct argument
)\, so some restriction is needed. We consider "primitive" axes\, in which
the left and right eigenspaces having eigenvalue 1 are one-dimensional. <
br>
Hall\, Rehren\, Shpectorov solves obtained a positive answer for c
ommutative axial algebras of "Jordan type" \\(\\lambda \\neq \\frac{1}{2}\
\)\, although the proof relies on the classification of simple groups and
the given bound of the dimension is rather high. Gorshkov and Staroletov p
rovided a sharp bound for 3-generated commutative axial algebras of "Jorda
n type". Our objective in this project is give a noncommutative version an
d indicate how to investigate 4-generated commutative axial algebras of "J
ordan type"\, in terms of the regular representation.
Our method
is to build an associative algebra from the adjoint algebra of \\(A\\)\, w
hich has a strictly larger dimension which nevertheless also is finite dim
ensional.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oksana Bezuschak (Kyiv Taras Shevchenko University\, Ukraine)
DTSTART:20211021T170000Z
DTEND:20211021T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/55
DESCRIPTION:Title: Locally matrix algebras and algebras of Mackey\nby Oksa
na Bezuschak (Kyiv Taras Shevchenko University\, Ukraine) as part of LieJo
r Online Seminar: Algebras\, representations\, and applications\n\n\nAbstr
act\nIn this talk we will discuss:\n\n1. Tensor decompositions of locally
matrix algebras and their parametrization by Steinitz numbers.\n\n2. Autom
orphisms and derivations of locally matrix algebras.\n\n3. Automorphisms a
nd derivations of Mackey algebras and Mackey groups. In particular\, we de
scribe automorphisms of all infinite simple finitary torsion groups (in th
e classification of J.Hall) and derivations of all infinite-dimensional si
mple finitary Lie algebras (in the classification of A.Baranov and H.Strad
e).\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aron Simis (Universidade Federal de Pernambuco\, Brazil)
DTSTART:20211028T170000Z
DTEND:20211028T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/56
DESCRIPTION:Title: Some conjectures in commutative algebra\nby Aron Simis
(Universidade Federal de Pernambuco\, Brazil) as part of LieJor Online Sem
inar: Algebras\, representations\, and applications\n\n\nAbstract\nThere a
re "big" conjectures and not-so-big ones in the field. Some of the first h
ave either been solved (often by unexpected tools) or are still pending li
ke a fruit on the top of a tree with delicate branches\, making it often h
ard for a layperson like some of us. This talk is about more modest conjec
tures\, at anyone's reach and pending from trees with more stable branches
. Some of these may have some interest in algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vsevolod Gubrev (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20211104T170000Z
DTEND:20211104T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/57
DESCRIPTION:Title: Embedding of Loday algebras into Rota-Baxter algebras\n
by Vsevolod Gubrev (Sobolev Institute of Mathematics\, Novosibirsk\, Russi
a) as part of LieJor Online Seminar: Algebras\, representations\, and appl
ications\n\n\nAbstract\nIt is known that every Rota-Baxter algebra of weig
ht 0 (1) gives rise to a prealgebra (postalgebra). In 2013\, it was proved
that every pre- or postalgebra injectively embeds into corresponding Rota
-Baxter algebra of weight 0 or 1 respectively. We study the structure and
the PBW-property of the universal enveloping Rota-Baxter algebra of a give
n pre- or post-Lie algebra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Grishkov (Universidade de São Paulo\, Brazil)
DTSTART:20211111T170000Z
DTEND:20211111T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/58
DESCRIPTION:Title: 12th Hilbert problem and Carlitz-Drinfeld-Anderson modules<
/a>\nby Alexandre Grishkov (Universidade de São Paulo\, Brazil) as part o
f LieJor Online Seminar: Algebras\, representations\, and applications\n\n
\nAbstract\nThe well known Kronecker-Weber theorem affirms that every fini
te abelian extension of the field \\(Q\\) of rational numbers belongs to
some cyclotomic extension \\(Q(t|t^n=1)\\). In his 12th problem D.Hilbert
asked how to generalize this theorem for other global fields. In this talk
\, we give the exposition of atual state of this problem together with th
e connection with Carlitz-Drinfeld-Anderson modules.
Recall that
Anderson module \\(M\\) is a (left)module over non-commutative ring \\(R=
C_p[T\,\\tau]\\)\, \\(T\\tau=\\tau T\\)\, \\(\\tau a=a^p \\tau\\)\, where
\\(C_p\\) is a some field of characteristic \\(p>0\\)\, such that \\(M\\)
is free finite generated over subrings \\(C_p[T]\\) and \\(C_p\\{\\tau\\}\
\).\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo Aguiar (Cornell University\, USA)
DTSTART:20211202T150000Z
DTEND:20211202T160000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/59
DESCRIPTION:Title: Lie theory relative to a hyperplane arrangement\nby Mar
celo Aguiar (Cornell University\, USA) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nA result due t
o Joyal\, Klyachko\, and Stanley relates free Lie algebras to partition la
ttices. We will discuss the precise relationship and interpret the result
in terms of the braid hyperplane arrangement. We will then extend this res
ult to arbitrary (finite\, real\, and central) hyperplane arrangements\, a
nd do the same with several additional aspects of classical Hopf-Lie theor
y. The Tits monoid of an arrangement\, and the notion of lune\, play centr
al roles in the discussion. This is joint work with Swapneel Mahajan.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sokolov (UFABC\, Brazil)
DTSTART:20211209T170000Z
DTEND:20211209T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/60
DESCRIPTION:Title: Non-Abelian Poisson brackets on projective spaces\nby V
ladimir Sokolov (UFABC\, Brazil) as part of LieJor Online Seminar: Algebra
s\, representations\, and applications\n\n\nAbstract\nWe discuss nonabelia
n Poisson structures on affine and projective spaces over \\(\\mathbb{C}\\
). We also construct a class of examples of nonabelian Poisson structures
on \\(\\mathbb{C} P^{n-1}\\) for \\(n>2\\). These nonabelian Poisson struc
tures depend on a modular parameter \\(\\tau\\in\\mathbb{C}\\) and an addi
tional discrete parameter \\(k\\in\\mathbb{Z}\\)\, where \\(1\\leq k< n
\\) and \\(k\,n\\) are coprime. The abelianization of these Poisson struct
ures can be lifted to the quadratic elliptic Poisson algebras \\(q_{n\,k}(
\\tau)\\).\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arturo Pianzola (University of Alberta\, Canada)
DTSTART:20211125T170000Z
DTEND:20211125T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/61
DESCRIPTION:Title: Derivations of twisted forms of Lie algebras\nby Arturo
Pianzola (University of Alberta\, Canada) as part of LieJor Online Semina
r: Algebras\, representations\, and applications\n\n\nAbstract\nThe main p
urpose of this talk is to explain how the theory of torsors can be used to
study problems in infinite dimensional Lie theory. I will not assume that
the audience is familiar with torsors. Definitions and examples will be g
iven. The main application in this case is to provide a general framework
(relative sheaves of Lie algebras) that explains/justifies a known result
about the derivations of multiloop algebras.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iryna Kashuba (Universidade de São Paulo\, Brazil)
DTSTART:20211202T170000Z
DTEND:20211202T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/62
DESCRIPTION:Title: On the Free Jordan algebras\nby Iryna Kashuba (Universi
dade de São Paulo\, Brazil) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nWe will discuss a conjec
ture for the character of the homogenous components of the free Jordan al
gebra on \\(d\\) generators as a \\(GL(d)\\)-module. This is joint work wi
th Olivier Mathieu.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Koshlukov (UNICAMP\, Brazil)
DTSTART:20220217T170000Z
DTEND:20220217T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/64
DESCRIPTION:Title: Gradings on upper triangular matrices\nby Plamen Koshlu
kov (UNICAMP\, Brazil) as part of LieJor Online Seminar: Algebras\, repres
entations\, and applications\n\n\nAbstract\nGradings on upper triangular m
atrices.\; Plamen Koshlukov (UNICAMP\, Brazil)\; The upper triangular matr
ix algebras are important in Linear Algebra\, and represent a powerful too
l in Ring Theory. They also appear in the theory of PI algebras.
In addition to the usual associative product\, one can consider the Lie br
acket and also the symmetric (Jordan) product on the upper triangular matr
ices.
We discuss the group gradings on the upper triangular matri
ces viewed as an associative\, Lie and Jordan algebra\, respectively. Vale
nti and Zaicev proved that the associative gradings are\, in a sense\, giv
en by gradings on the matrix units. Di Vincenzo\, Valenti and Koshlukov cl
assified such gradings. Later on\, Yukihide and Koshlukov\, described the
Lie and the Jordan gradings. In this talk we recall some of these results
as well as a new development in a rather general setting\, obtained by Yuk
ihide and Koshlukov.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Holger Petersson (FernUniversität in Hagen\, Germany)
DTSTART:20220224T170000Z
DTEND:20220224T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/65
DESCRIPTION:Title: Octonions and Albert algebras over commutative rings\nb
y Holger Petersson (FernUniversität in Hagen\, Germany) as part of LieJor
Online Seminar: Algebras\, representations\, and applications\n\n\nAbstra
ct\nIn the first part of the lecture\, I will focus on two properties of o
ctonion algebras that are known to hold over fields but fail over arbitrar
y commutative rings: their enumeration by means of the Cayley-Dickson cons
truction\, and the norm equivalence theorem. In the second part\, I will d
escribe a new approach to the first Tits construction of Albert algebras t
hat\, even over fields\, is more general than the classical one and sheds
some new light on the classification problem for reduced Albert algebras o
ver commutative rings.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Racine (Ottawa University\, Canada)
DTSTART:20220303T170000Z
DTEND:20220303T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/66
DESCRIPTION:Title: Lie Algebras afforded by Jordan algebras with particular At
tention to Albert Algebras\nby Michel Racine (Ottawa University\, Cana
da) as part of LieJor Online Seminar: Algebras\, representations\, and app
lications\n\n\nAbstract\nGiven a (quadratic) Jordan algebra J over a ring
k\, one obtains three Lie algebras\, the derivation algebra\, the structur
e algebra\, and the Tits algebra. We are particularly interested in the ca
se where J is an Albert algebra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Guerassimov (UFMG\, Brazil)
DTSTART:20220310T170000Z
DTEND:20220310T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/67
DESCRIPTION:Title: Random walks on groups. An introduction\nby Victor Guer
assimov (UFMG\, Brazil) as part of LieJor Online Seminar: Algebras\, repre
sentations\, and applications\n\n\nAbstract\nGeometric methods proved to b
e useful in the study of some groups. However the geometry of the Cayley g
raph of a group is rather different from the geometry of classical geometr
ic objects such as homogeneous spaces of Lie groups. The similarity betwee
n these two geometries grows as the scale of observation increases. And th
e asymptototic behavior of them shows surprising similarity. Random walks
is an essential tool in studying large-scale geometry of groups. On the ot
her hand it is an interesting object for probabilists since many propertie
s of general stochastic processes are manifested here in a rather simple f
orm. In my talk\, I will provide an elementary introduction to this vast a
rea. No special knowledge beyond the usual university mathematics is requi
red.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Stolin (Chalmers University of Technology\, Sweden)
DTSTART:20220317T170000Z
DTEND:20220317T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/68
DESCRIPTION:Title: 40 years of Lie bialgebras: From definition to classificati
on\nby Alexander Stolin (Chalmers University of Technology\, Sweden) a
s part of LieJor Online Seminar: Algebras\, representations\, and applicat
ions\n\n\nAbstract\nThe history of Lie bialgebras began with the paper whe
re the Lie bialgebras were defined: V. G. Drinfeld\, "Hamiltonian structur
es on Lie groups\, Lie bialgebras and the geometric meaning of the classic
al Yang-Baxter equations"\, Dokl. Akad. Nauk SSSR\, 268:2 (1983) Presented
: L.D. Faddeev. Received: 04.06.1982.
The aim of my talk is to ce
lebrate 40 years of Lie bialgebras in mathematics and to explain how these
important algebraic structures can be classified. This classification goe
s "hand in hand" with the classification of the so-called Manin triples an
d Drinfeld doubles also introduced in Drinfeld's paper cited above.
The ingenious idea how to classify Drinfeld doubles associated with Lie
algebras possessing a root system is due to F. Montaner and E. Zelmanov.
In particular\, using their approach the speaker classified Lie bialgeras\
, Manin triples and Drinfeld doubles associated with a simple finite dimen
sional Lie algebra g (the paper was based on a private communication by E.
Zelmanov and it was published in Comm. Alg. in 1999).
Further\,
in 2010\, F. Montaner\, E. Zelmanov and the speaker published a paper in
Selecta Math.\, where they classified Drinfeld doubles on the Lie algebra
of the formal Taylor power series g[[u]] and all Lie bialgebra structures
on the polynomial Lie algebra g[u].
Finally\, in March 2022 S. M
aximov\, E. Zelmanov and the speaker published an Arxive preprint\, where
they made a crucial progress towards a complete classification of Manin t
riples and Lie bialgebra structures on g[[u]].
Of course\, it is
impossible to compress a 40 years history of the subject in one talk but
the speaker will try his best to do this.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuriy A. Drozd (Kiev University\, Ukraine)
DTSTART:20220324T170000Z
DTEND:20220324T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/69
DESCRIPTION:Title: Morita Theory for noncommutative varieties\nby Yuriy A.
Drozd (Kiev University\, Ukraine) as part of LieJor Online Seminar: Algeb
ras\, representations\, and applications\n\n\nAbstract\nMorita theorem giv
es a criterion of equivalence of categories of modules over rings. On the
other hand\, Gabriel proved that the category of coherent sheaves defines
a Noetherian scheme up to isomorphism. We have established a result which
is in a sense\, a union and a combination of these two theorems. Namely\,
we show that the category of coherent sheaves over a Noetherian non-commut
ative scheme completely defines its center and the schemes with the same c
enter are Morita equivalent if and only if one of them is isomorphic to th
e scheme of endomorphisms of a local progeneretor of the other.
It is
a common work with Igor Burban.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio M. Peralta (Universidad de Granada\, Spain)
DTSTART:20220331T170000Z
DTEND:20220331T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/70
DESCRIPTION:Title: How can we apply Jordan structures to reinterpret Wigner-Uh
lhorn theorem?\nby Antonio M. Peralta (Universidad de Granada\, Spain)
as part of LieJor Online Seminar: Algebras\, representations\, and applic
ations\n\n\nAbstract\nUp to date\, much has been written about E. Wigner a
nd U. Uhlhron theorems and their importance for physics and mathematics. F
or the sake of conciseness\, let us go straight to some of the starring re
sults. There are six mathematical models employed in quantum mechanics\, a
mong them we have:- The C\\(^*\\)-algebra \\(B(H)\\) of bounded oper
ators;
- The Jordan algebra \\(B(H)_{sa}\\) of bounded self-
adjoint operators;
- The orthomodular lattice \\(\\mathbf{L}
\\) of closed subspaces of \\(H\\)\, equivalently\, the lattice of all pro
jections in \\(B(H)\\)\,
where \\(H\\) is a complex Hilbert space.
The natural automorphisms of these mathematical models (i.e.\, the bi
jections \\(f\\) on these sets preserving the corresponding relevant struc
ture: associative product and involution\, Jordan product\, and orthogonal
ity and order between subspaces or projections) represent the symmetry gro
ups of quantum mechanics and are endowed with natural topologies induced b
y the probabilistic structure of quantum mechanics. It is known that these
symmetry groups are all isomorphic when dim\\((H)\\geq 3\\). The last res
triction exclude rank two\, where there are no more than two orthogonal pr
ojections. This equivalence can be seen as the celebrated Wigner unitary-a
ntiunitary theorem.
By replacing the set of projections \\(\\mathca
l{P}(H)\\) by the wider set\, \\(PI(H) = \\mathcal{U}(B(H))\\)\, of all p
artial isometries on \\(H\\)\, L. Molná proved in [3] the following re
sult: Let \\(H\\) be a complex Hilbert space with dim\\((H)\\geq 3\\). Sup
pose that \\(\\Phi : \\mathcal{U}(B(H))\\to \\mathcal{U}(B(H))\\) is a bij
ective transformation which preserves the natural partial ordering and the
orthogonality between partial isometries in both directions. If \\(\\Phi\
\) is continuous (in the operator norm) at a single element of \\(\\mathca
l{U}(B(H))\\) different from \\(0\\)\, then \\(\\Phi\\) extends to a real
linear triple isomorphism. %Here we consider the standard partial ordering
on \\(PI(H)\\) given by \\( e\\leq u\\) if and only if \\(u-e\\) is a par
tial isometry orthogonal to \\(e\\).
During this talk we shall pres
ent new results\, obtained in collaboration with Y. Friedman (see [1])\, s
howing that an extension of the previous results is possible in the case o
f a bijection between the lattices of tripotents of two Cartan factors and
atomic JBW\\(^*\\)-triples non-containing rank-one Cartan factors. These
new result provide new models to understand the quantum models. We shall a
lso see how the results provide new alternatives to complement recent stud
ies by J. Hamhalter [2] proving that the set of partial isometries with i
ts partial order and orthogonality relation is a complete Jordan
invariant for von Neumann algebras.
References
[1] Y.
Friedman\, A.M. Peralta\, Representation of symmetry transformations on t
he sets of tripotents of spin and Cartan factors\, to appear in Analysi
s and Mathematical Physics\, https://doi.org/10.1007/s13324-021-00644
-8\, arXiv: 2101.00670.
[2] J. Hamhalter\, Dye's theorem for tripotents
in von Neumann algebras and JBW\\(^*\\)-triples\, Banach J. Math. Anal
. 15 (2021)\, no. 3\, Paper No. 49\, 19 pp.
[3] L. Molná
r\, On certain automorphisms of sets of partial isometries\, Arch. Math
. (Basel) 78\, no. 1\, 43--50 (2002).
[4] U. Uhlhorn\, Repre
sentation of symmetry transformations in quantum mechanics\, Ark. Fysik
23\, 307--340 (1963).
[5] E.P. Wigner\, Gruppentheorie u
nd ihre Anwendung auf die Quantenmechanik der Atomspektrum\, Fredrik V
ieweg und Sohn\, 1931.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Shumyatsky (UnB\, Brazil)
DTSTART:20220407T170000Z
DTEND:20220407T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/71
DESCRIPTION:Title: Commuting probability for subgroups of a finite group\n
by Pavel Shumyatsky (UnB\, Brazil) as part of LieJor Online Seminar: Algeb
ras\, representations\, and applications\n\n\nAbstract\nThis is a joint wo
rk with Eloisa Detomi (University of Padova).
If \\(K\\) is a sub
group of a finite group \\(G\\)\, the probability that an element of \\(G\
\) commutes with an element of \\(K\\) is denoted by \\(Pr(K\,G)\\). The p
robability that two randomly chosen elements of \\(G\\) commute is denoted
by \\(Pr(G)\\). A well known theorem\, due to P. M. Neumann\, says that i
f \\(G\\) is a finite group such that \\(Pr(G)\\geq\\epsilon\\)\, then \\(
G\\) has a nilpotent normal subgroup \\(T\\) of class at most \\(2\\) such
that both the index \\([G:T]\\) and the order \\(|[T\,T]|\\) are \\(\\eps
ilon\\)-bounded.
In the talk we will discuss a stronger version
of Neumann's theorem: if \\(K\\) is a subgroup of \\(G\\) such that \\(Pr(
K\,G)\\geq\\epsilon\\)\, then there is a normal subgroup \\(T\\leq G\\) an
d a subgroup \\(B\\leq K\\) such that the indexes \\([G:T]\\) and \\([K:B]
\\) and the order of the commutator subgroup \\([T\,B]\\) are \\(\\epsilon
\\)-bounded.
We will also discuss a number of corollaries of thi
s result. A typical application is that if in the above theorem \\(K\\) is
the generalized Fitting subgroup \\(F^*(G)\\)\, then \\(G\\) has a class-
2-nilpotent normal subgroup \\(R\\) such that both the index \\([G:R]\\) a
nd the order of the commutator subgroup \\([R\,R]\\) are \\(\\epsilon\\)-b
ounded.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo do Nascimento Marcos (IME-USP\, Brazil)
DTSTART:20220414T170000Z
DTEND:20220414T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/72
DESCRIPTION:Title: Koszul e homogeneous triples for algebras with two relation
s\nby Eduardo do Nascimento Marcos (IME-USP\, Brazil) as part of LieJo
r Online Seminar: Algebras\, representations\, and applications\n\n\nAbstr
act\nThis talk is based on a joint work with Yury Volkov. We define the ca
tegory of homogeneous triples\, which is equivalent to the category of gra
ded algebras\, with a fixed semisimple degree zero part. We apply the resu
lts to algebras whose defining ideal has two generators\, and give a parti
al classification.
We thank Fapesp\, grant 2018/23690-6\, for th
e support.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Miasnikov (Stevens Institute of Technology\, USA)
DTSTART:20220421T170000Z
DTEND:20220421T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/73
DESCRIPTION:Title: Rich groups and weak second order logic\nby Alexei Mias
nikov (Stevens Institute of Technology\, USA) as part of LieJor Online Sem
inar: Algebras\, representations\, and applications\n\n\nAbstract\n"What c
an one describe by first-order formulas in a given group A?" - is an old a
nd interesting question. Of course\, this depends on the group A. For exam
ple\, in a free group only cyclic subgroups (and the group itself) are def
inable in the first-order logic\, but in a free monoid of finite rank any
finitely generated submonoid is definable. A group A is called rich if the
first-order logic in A is equivalent to the weak second order logic. Surp
risingly\, there are a lot of interesting groups\, rings\, semigroups\, et
c.\, which are rich. I will describe various algebraic\, geometric\, and a
lgorithmic properties that are first-order definable in rich groups and ap
ply these to some open problems. Weak second order logic can be introduced
into algebraic structures in different ways: via HF-logic\, or list super
structures over A\, or computably enumerable infinite disjunctions and con
junctions\, or via finite binary predicates\, etc. I will describe a parti
cular form of this logic which is especially convenient to use in algebra
and show how to effectively translate such weak second order formulas into
the equivalent first-order ones in the case of a rich group A.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Sapir (Vanderbilt University\, USA)
DTSTART:20220428T170000Z
DTEND:20220428T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/74
DESCRIPTION:Title: Subgroups of the R.Thompson group F\nby Mark Sapir (Van
derbilt University\, USA) as part of LieJor Online Seminar: Algebras\, rep
resentations\, and applications\n\n\nAbstract\nThis is joint work with Gil
i Golan-Polak. We describe the so-called closed subgroups of F. In particu
lar\, we construct a subgroup of F with easily decidable membership proble
m and undecidable conjugacy problem\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Penkov (Jacobs University Bremen\, Germany)
DTSTART:20220505T170000Z
DTEND:20220505T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/75
DESCRIPTION:Title: New analogues of category O for the Lie algebra \\(sl(\\inf
ty)\\)\nby Ivan Penkov (Jacobs University Bremen\, Germany) as part of
LieJor Online Seminar: Algebras\, representations\, and applications\n\n\
nAbstract\nI will recall several highest weight categories for \\(sl(\\inf
ty)\\) studied in the past decade\, and will then report on the newest hig
hest weight categories introduced by P. Zadunaisky. A main point is the us
e a non-obvious Borel subalgebra plus a semi-large annihilator condition.
As a side effect\, the new categories produce interesting and challenging
combinatorics.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bahturin (Memorial University of Newfoundland\, Canada)
DTSTART:20220512T170000Z
DTEND:20220512T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/76
DESCRIPTION:Title: Group Gradings and Actions of Pointed Hopf Algebras\nby
Yuri Bahturin (Memorial University of Newfoundland\, Canada) as part of L
ieJor Online Seminar: Algebras\, representations\, and applications\n\n\nA
bstract\nPointed Hopf algebras are a wide class of Hopf algebras\, includi
ng group algebras and enveloping algebras of Lie algebras. In this talk\,
based on a recent work with Susan Montgomery\, we study actions of pointed
Hopf algebras on simple algebras. These actions are known to be inner\, a
s in the case of Skolem - Noether theorem. We try to give explicit descrip
tions\, whenever possible\, and consider Taft algebras\, their Drinfeld do
ubles and some quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Oswaldo Lezama Serrano (Universidad Nacional de Colombia\, C
olombia)
DTSTART:20220519T170000Z
DTEND:20220519T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/77
DESCRIPTION:Title: Algebraic sets\, ideals of points and the Hilbert's Nullste
llensatz theorem for skew PBW extensions\nby José Oswaldo Lezama Serr
ano (Universidad Nacional de Colombia\, Colombia) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nIn
this talk we define the algebraic sets and the ideal of points for bijecti
ve skew PBW extensions with coefficients in left Noetherian domains. Some
properties of affine algebraic sets of commutative algebraic geometry will
be extended\, in particular\, a Zariski topology will be constructed. Ass
uming additionally that the extension is quasi-commutative with polynomial
center and the ring of coefficients is an algebraically closed field\, we
will prove an adapted version of Hilbert's Nullstellensatz theorem that c
overs the classical one. The Gröbner bases of skew PBW extensions will be
used for defining the algebraic sets and for proving the main theorem. Ma
ny key algebras and rings coming from mathematical physics and non-commuta
tive algebraic geometry are skew PBW extensions.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Efim Zelmanov (University of California\, San Diego\, USA)
DTSTART:20220526T170000Z
DTEND:20220526T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/78
DESCRIPTION:by Efim Zelmanov (University of California\, San Diego\, USA)
as part of LieJor Online Seminar: Algebras\, representations\, and applica
tions\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David A. Jordan (Sheffield University\, UK)
DTSTART:20220602T170000Z
DTEND:20220602T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/79
DESCRIPTION:Title: Skew derivations of quantum spaces\nby David A. Jordan
(Sheffield University\, UK) as part of LieJor Online Seminar: Algebras\, r
epresentations\, and applications\n\n\nAbstract\nLet $n$ be a positive int
eger and let $Q = (q_{ij})$ be a multipicatively antisymmetric $n \\times
n$ matrix\nover a field $\\mathbb{K}$\, that is $q_{ii}=1$ for $1\\leq i
\\leq n$ and\, for $1\\leq i\,j\\leq n$\, $q_{ij}\\neq 0$ and $q_{ji}=q_{
ij}^{-1}$. \nThe quantized (co-ordinate ring of) quantum
$n$-space $R:=\\mathcal{O}_Q(\\mathbb{K}^n)$ is the $\\mathbb{K}$-alg
ebra generated by $x_1\,x_2\,\\dots\, x_n$\nsubject to the relations $x_ix
_j = q_{ij}x_jx_i$ for $1 \\leq i < j \\leq n$.\n\nAlthough the space of d
erivations $\\mathrm{Der}(R)$ is well-understood through work of Alev and
Chamarie in 1982\, less is known about the \nspace $\\mathrm{Der}_\\sigma(
R)$ of $\\sigma$-derivations of $R$. The only case in the literature wh
ere the $\\sigma$-derivations of $R$ are determined appears to be when $n=
2$ and\, for some $\\lambda\\in \\mathbb{K}^*$\, $\\sigma(x_1)=\\lambda x_
1$ and $\\sigma(x_2)=\\lambda^{-1} x_2$. \nThis case appears in a 2018 pap
er by Almulhem and Brzezi\\'{n}ski that was motivated by differential geom
etry. This talk will discuss the classification of the \n$\\sigma$-derivat
ions of $R$\n for all $n$ when $\\sigma$ is toric\, that is each $
x_i$ is an eigenvector for $\\sigma$\, with a view to applications to iter
ated Ore extensions of $\\mathbb{K}$. Any such classification must includ
e the inner $\\sigma$-derivations of $R$\, that is those for which
there exists $a\\in R$ such that $\\delta_a(r)=ar-\\sigma(r)a$ for all $r\
\in R$.\n\nThe methods are based on two of the classical methods of noncom
mutative algebra namely localization and grading\, in this case by $\\math
bb{Z}^n$. Localization at the set $\\{x_1^{d_1}x_2^{d_2}\\dots x_n^{d_n}\\
}$ yields the quantum $n$-torus $T:=\\mathcal{O}_Q((\\mathbb{K}^*)^
n)$ to which $\\sigma$ and all $\\sigma$-derivations extend. A $\\sigma$-d
erivation $\\delta$ of $T$ is homogeneous\, of weight $(d_1\,d_2\,\
\dots\, d_n)$\, if $\\delta(x_i)\\in \\mathbb{K} x_1^{d_1}x_2^{d_2}\\dots\
,x_i^{d_i+1}\\dots x_n^{d_n}$ for $1\\leq i\\leq n$ and every $\\sigma$-de
rivation of $T$ is a unique linear combination of homogeneous $\\sigma$-de
rivations. It turns out that if $\\delta$ is a homogeneous $\\sigma$-deriv
ation of $T$ then either the automorphism $\\sigma$ is inner or the $\\sig
ma$-derivation $\\delta$ is inner and the Ore extension $T[x\;\\sigma\,\\d
elta]$ can\, by a change of variables\, be expressed as an Ore extension o
f either automorphism type or derivation type. This dichotomy influences t
he space\n$\\mathrm{Der}_\\sigma(R)$ which can be identified with $\\{\\de
lta\\in \\mathrm{Der}_\\sigma(T) :\\delta(R)\\subseteq R\\}$. The most obv
ious $\\sigma$-derivations included here are\nthe homogeneous $\\sigma$-de
rivations of weight $(d_1\,d_2\,\\dots\, d_n)$ where each $d_i\\geq 0$\, b
ut more interesting are those for which one $d_i=-1$. There are two types
of these\, depending on whether $\\sigma$ or $\\delta$ is inner on $T$. In
the latter case we are in a common situation where a $\\sigma$-derivation
of a ring $R$ is not inner on $R$ but becomes inner on the localization o
f $R$ at the powers of a normal element of $R$\, giving rise to a distingu
ished normal or central element of the Ore extension $R[x\;\\sigma\,\\delt
a]$.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (Université de Strasbourg\, France)
DTSTART:20220609T170000Z
DTEND:20220609T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/80
DESCRIPTION:Title: New examples of Nielsen-Schreier varieties of algebras\
nby Vladimir Dotsenko (Université de Strasbourg\, France) as part of LieJ
or Online Seminar: Algebras\, representations\, and applications\n\n\nAbst
ract\nA variety of algebras is said to be a Nielsen-Schreier variety if ev
ery subalgebra of every free algebra is free. Using methods of the operad
theory\, we propose an effective combinatorial criterion for that property
in the case of algebras over a field of zero characteristic. Using this c
riterion\, we show\, in particular\, that the variety of all pre-Lie algeb
ras (also known as right-symmetric algebras) is Nielsen-Schreier\, and tha
t\, quite surprisingly\, there are already infinitely many Nielsen-Schreie
r varieties of algebras with one binary operation and identities of degree
three. This is joint work with with Ualbai Umirbaev.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT\, USA)
DTSTART:20220616T170000Z
DTEND:20220616T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/81
DESCRIPTION:Title: Weak Jordan algebras in characteristic 5 and tensor categor
ies\nby Pavel Etingof (MIT\, USA) as part of LieJor Online Seminar: Al
gebras\, representations\, and applications\n\n\nAbstract\nWe propose a ne
w algebraic structure\, called a weak Jordan algebra\, which we define out
side of characteristics 2\,3. Any Jordan algebra is a weak Jordan algebra\
, and the converse holds in characteristics different from 5. However\, in
characteristic 5 there are many examples of simple weak Jordan algebras w
hich are not Jordan\, and not even power associative - they are only power
associative up to degree 5 (note that by a theorem of Albert\, an algebra
in characteristic 0 or >=7 which is power associative up to degree 5 and
even 4 is power associative in all degrees). These algebras correspond (vi
a a version of the Kantor-Koehler-Tits construction) to Lie algebras in th
e Fibonacci tensor category Fib in characteristic 5\, which can be obtaine
d from Lie algebras in characteristic 5 with a derivation d such that \\(d
^5=0\\) by the procedure of semisimplification. This allows one to view th
e notion of a weak Jordan algebra as an example from a new subject that ma
y be called "Lie theory in tensor categories".
This is joint work
with A. Kannan and V. Ostrik.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Dokuchaev (IME-USP (Brazil))
DTSTART:20220623T170000Z
DTEND:20220623T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/82
DESCRIPTION:Title: Strong equivalence of graded algebras\nby Misha Dokucha
ev (IME-USP (Brazil)) as part of LieJor Online Seminar: Algebras\, represe
ntations\, and applications\n\n\nAbstract\nWe introduce the notion of a st
rong equivalence between graded algebras and prove that any partially-stro
ngly-graded algebra by a group G is strongly-graded-equivalent to the skew
group algebra by a product partial action of G. We show that strongly-gra
ded-equivalence preserves strong gradings and is nicely related to Morita
equivalence of product partial actions. Furthermore\, we show that strongl
y-graded-equivalent partially-strongly-graded algebras with orthogonal loc
al units are stably isomorphic as graded algebras. This is a part of a joi
nt preprint with Fernando Abadie and Ruy Exel.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Lopez-Permouth (Ohio University\, USA)
DTSTART:20220630T170000Z
DTEND:20220630T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/83
DESCRIPTION:Title: On the isomorphism problem for basic modules\nby Sergio
Lopez-Permouth (Ohio University\, USA) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nWhile mutual
congeniality of bases has been known to guarantee that basic modules from
so related bases are isomorphic\, the question of what can be said about i
somorphism of basic modules in general has remained open. We show that nei
ther of two possible extremes must hold. For some algebras\, it is possibl
e\, for basic modules to be non-isomorphic. Also\, it is possible\, for s
ome algebras\, that all basic modules be isomorphic.
We show that
there are at least as many pairwise non-isomorphic basic modules over the
\\(F\\)-algebra \\(F[x]\\) of polynomials in a single variable as there ar
e elements in \\(F\\). We show that basic modules over \\(F[x]\\) can be
non-isomorphic when they are induced by discordant bases and also even whe
n there is a (non-mutual) congeniality among them. In the process and as a
byproduct\, we introduce the notion of domains of divisibility of modules
over arbitrary rings and explore some of the properties of a divisibility
profile.
At the opposite end of the spectrum\, we present an alge
bra where all basic modules are isomorphic\, regardless of congeniality.
This is a report on joint work with: C. Arellano\, P. Aydogdu\, R.
Muhammad\, and M. Zailaee.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Ezequiel Angiono (National University of Cordoba\, Argentina)
DTSTART:20220707T170000Z
DTEND:20220707T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/84
DESCRIPTION:Title: Finite-dimensional pointed Hopf algebras over central exten
sions of abelian groups\nby Ivan Ezequiel Angiono (National University
of Cordoba\, Argentina) as part of LieJor Online Seminar: Algebras\, repr
esentations\, and applications\n\n\nAbstract\nOne of the most studied kind
s of finite-dimensional Hopf algebras is the family of pointed ones: it me
ans that the coradical is the algebra of the group-like elements. When the
group is abelian\, all such examples are known following the so-called Li
fting Method by Andruskiewitsch-Schneider and include deformations of smal
l quantum groups\, their super analogues and some exceptional examples of
Nichols algebras. When the group is not abelian\, the classification is no
t known yet. Even more\, the first step of the Lifting Method (the computa
tion of all finite-dimensional Nichols algebras) has not been completed: t
he classification has been performed by Heckenberger-Vendramin when the el
ements in degree one form a non-simple Yetter-Drinfeld module\, and consis
t of low rank exceptions and large rank families.\n\nIn this talk we will
present finite-dimensional Hopf algebras whose coradical is the group alge
bra of a central extension of an abelian group. They fall into families as
sociated with a simple Lie algebra together with a Dynkin diagram automorp
hism.\n\nWe will show conversely that every finite-dimensional pointed Hop
f algebra over a non-abelian group with a non-simple infinitesimal braidin
g is of this form for large rank families. The proof follows the steps of
the Lifting Method. Indeed we prove that the large rank families are cocyc
le twists of Nichols algebras constructed by Lentner as foldings of Nichol
s algebras of Cartan type over abelian groups by outer automorphisms. This
enables us to give uniform Lie-theoretic descriptions of the large rank f
amilies\, prove generation in degree one and construct liftings.\n\nWe als
o show that every lifting is a cocycle deformation of the corresponding co
radically graded Hopf algebra using an explicit presentation by generators
and relations of the Nichols algebra.\n\nThe talk is based on a joint wor
k with Simon Lentner and Guillermo Sanmarco.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell (University of Waterloo\, Canada)
DTSTART:20220728T170000Z
DTEND:20220728T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/85
DESCRIPTION:Title: Recent results on the Dixmier-Moeglin equivalence\nby J
ason Bell (University of Waterloo\, Canada) as part of LieJor Online Semin
ar: Algebras\, representations\, and applications\n\n\nAbstract\nDixmier a
nd Moeglin showed that if \\(L\\) is a finite-dimensional complex Lie alge
bra then the primitive ideals of the enveloping algebra \\(U(L)\\) are the
prime ideals of \\({\\rm Spec}(U(L))\\) that are locally closed in the Za
riski topology. In addition\, they proved that a prime ideal \\(P\\) of \\
(U(L)\\) is primitive if and only if the Goldie ring of quotients of \\(U(
L)/P\\) has the property that its centre is just the base field of the com
plex numbers. Algebras that share this characterization of primitive ideal
s are said to satisfy the Dixmier-Moeglin equivalence. We give an overvie
w of this property and mention some recent work on proving this equivalenc
e holds for certain classes of twisted homogenous coordinate rings and cla
sses of Hopf algebras of small Gelfand-Kirillov dimension.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruy Exel (UFSC\, Brazil)
DTSTART:20220804T170000Z
DTEND:20220804T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/86
DESCRIPTION:Title: The opaque ideal\nby Ruy Exel (UFSC\, Brazil) as part o
f LieJor Online Seminar: Algebras\, representations\, and applications\n\n
\nAbstract\nGiven a C*-algebra \\(B\\)\, and a regular\, abelian\, sub-C*-
algebra \\(A\\subseteq B\\)\, we will discuss the opaque ideal \\(\
\Delta \\trianglelefteq B\\)\, which is a somewhat mysterious ideal that t
ends to vanish most of the time\, but not always. In the last part of th
e talk I will give an example of a non-vanishing opaque ideal based on an
idea of Rufus Willett\, and related to the celebrated action of the free g
roup on the 2-sphere used by Banach and Tarski to produce their paradox. T
his is based on joint work with David Pitts and Vrej Zarikian.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Sviridova (UnB\, Brazil)
DTSTART:20220714T170000Z
DTEND:20220714T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/87
DESCRIPTION:Title: Hook theorem for identities and its generalizations\nby
Irina Sviridova (UnB\, Brazil) as part of LieJor Online Seminar: Algebras
\, representations\, and applications\n\n\nAbstract\nHook theorem is one o
f the key result of the classical theory of polynomial identities of algeb
ras in the case of a field of characteristic zero. This well known result
is fundamental for applications of the technique of the classic representa
tion theory of the symmetric group to study identities. It has essential c
onnections with many important facts of PI-theory\, and implies many impor
tant and interesting consequences. In particular\, it is one of the basic
results for Kemer's positive solution of the Specht problem. Also it is th
e base to construct the growth theory for varieties of associative algebra
s over a field of of characteristic zero.\n\nIn the last years\, one of th
e most popular directions of the theory of polynomial identities is to con
sider algebras with some additional structures (such as gradings\, involut
ions\, actions by automorphisms\, etc.)\, and to study identities of such
algebras with the additional signature.\n\nWe will discuss the versions of
the hook theorem for various types of such identities with complementary
structures. In particular\, we will represent some version of the hook the
orem for identities with some types of actions. This result generalizes th
e analogous results known before\, for example\, for graded identities or
identities with involution. We also will discuss some possible consequence
s and applications of this theorem.\n\nThe talk is based on a joint work w
ith Renata Alves da Silva.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Elduque (Universidad de Zaragoza\, Spain)
DTSTART:20220818T170000Z
DTEND:20220818T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/88
DESCRIPTION:Title: Tensor categories\, algebras\, and superalgebras\nby Al
berto Elduque (Universidad de Zaragoza\, Spain) as part of LieJor Online S
eminar: Algebras\, representations\, and applications\n\n\nAbstract\nAfter
reviewing the basic definitions of tensor categories and the notion of se
misimplification of symmetric tensor categories\, it will be shown how the
semisimplification of the category of representations of the cyclic group
of order 3 over a field of characteristic 3 is naturally equivalent to th
e category of vector superspaces over this field. This allows to define a
superalgebra starting with any algebra endowed with an order 3 automorphis
m. As a noteworthy example\, the exceptional composition superalgebras wil
l be obtained\, in a systematic way\, from the split octonion algebra.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Lopatin (UNICAMP\, Brazil)
DTSTART:20220811T170000Z
DTEND:20220811T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/89
DESCRIPTION:Title: Separating invariants for matrices\, octonions and multisym
metric polynomials\nby Artem Lopatin (UNICAMP\, Brazil) as part of Lie
Jor Online Seminar: Algebras\, representations\, and applications\n\n\nAbs
tract\nIn 2002 Derksen and Kemper introduced the notion of separating inva
riants as a weaker concept than generating invariants. Roughly speaking\,
separating invariants "separate'' exactly the same orbits that are separat
ed by all polynomial invariants. There always exists a finite separating s
et whereas it is not the case for generating invariants. Moreover\, in man
y cases separating invariant less depend on the characteristic of the base
field than generating sets. This talk is dedicated to - joint res
ults with Gregor Kemper and Fabian Reimers on separating invariants for th
e ring of multisymmetric polynomials in \\(m\\) sets of \\(n\\) variables
over an arbitrary field \\(\\mathbb{F}\\);
- joint results with Alex
ander Zubkov on separating invariants of several octonions with respect to
the action of \\(G_2\\);
- joint results with Felipe Barbosa Cavalc
ante on separating invariants of \\(2\\times 2\\) and \\(3\\times 3\\) mat
rices.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Petrogradsky (UnB\, Brazil)
DTSTART:20220825T170000Z
DTEND:20220825T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/90
DESCRIPTION:Title: Growth in Lie algebras\nby Victor Petrogradsky (UnB\, B
razil) as part of LieJor Online Seminar: Algebras\, representations\, and
applications\n\n\nAbstract\nDifferent versions of Burnside Problem ask what one can say about finitely ge
nerated periodic groups under additional assumptions. For associative alge
bras\, Kurosh type problems ask
similar questions about properties of finitely generated nil (more genera
lly\, algebraic) algebras. Similarly\, one considers finitely generated re
stricted Lie algebras with a nil \\(p\\)-mapping. Now we study an oscillating intermediate growth in nil restricted Lie algebras.
<
br>Namely\, for any field of positive characteristic\, we construct a fami
ly of 3-generated restricted Lie algebras of intermediate oscillating grow
th. We call them Phoenix algebras\, because of the following.
a)
For infinitely many periods of time the algebra is "almost dying" by hav
ing a quasi-linear growth\, namely the lower Gelfand-Kirillov dimen
sion is one\, more precisely\, he growth is of type \\(n \\big(\\underbra
ce{\\ln\\cdots \\ln}_{q\\ \\text{times}} n\\big )^{\\kappa}\\)\, where \\
(q\\in\\mathbb N\\)\, \\(\\kappa>0\\) are constants.
b) On the other ha
nd\, for infinitely many \\(n\\) the growth function has a rather fast int
ermediate behaviour of type \\(\\exp( n/ (\\ln n)^{\\lambda})\\)\, \\(\\la
mbda\\) being a constant determined by characteristic\, for such periods t
he algebra is "resuscitating".
c) Moreover\, the growth function is bou
nded and oscillating between these two types of behaviour.
d) These res
tricted Lie algebras have a nil \\(p\\)-mapping.
We also construct
nil Lie superalgebras and nil Jordan superalgebras of similar oscillating
intermediary growth over arbitrary field.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa\, Canada)
DTSTART:20220901T170000Z
DTEND:20220901T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/91
DESCRIPTION:Title: Diagratification\nby Alistair Savage (University of Ott
awa\, Canada) as part of LieJor Online Seminar: Algebras\, representations
\, and applications\n\n\nAbstract\nWe will explain how one can construct d
iagrammatic presentations of categories of representations of Lie groups a
nd their associated quantum groups using only a small amount of informatio
n about these categories. To illustrate the technique in concrete terms\,
we will focus on the exceptional Lie group of type F4.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Berele (De Paul University\, USA)
DTSTART:20220922T170000Z
DTEND:20220922T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/92
DESCRIPTION:Title: Poincaré Series of the Trace Rings of Generic Matrices
\nby Allan Berele (De Paul University\, USA) as part of LieJor Online Semi
nar: Algebras\, representations\, and applications\n\n\nAbstract\nWe first
give some background on the Poincare series of the algebra of generic mat
rices and its associated trace ring\, and then focus on some recent work\,
including a conjecture for the denominator of the one variable series for
the trace rings. Time permitting we will also say a bit about traces of d
irect sums.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Facchini (Università degli Studi di Padova\, Italia)
DTSTART:20220929T170000Z
DTEND:20220929T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/93
DESCRIPTION:Title: Multiplicative lattices\, skew braces\nby Alberto Facch
ini (Università degli Studi di Padova\, Italia) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nThe
multiplicative lattices we will consider are those defined in the paper [3
]\, published in February 2022. Multiplicative lattices yield the natural
setting in which several basic mathematical questions concerning algebraic
structures find their answer (Zariski spectrum\, nilpotency\, solvability
\, abelian algebraic structures\,...) We will consider the particular case
of skew braces\, which appear in connection to the study of the Yang-Baxt
er equation ([2]\, [3] and [4]).\n\n[1] D. Bourn\, A. Facchini and M. Pomp
ili\, Aspects of the Category SKB of Skew Braces\, submitted for publicati
on\, available in arXiv\, 2022\n\n[2] A. Facchini\, Algebraic structures f
rom the point of view of complete multiplicative lattices\, accepted for p
ublication in ``Rings\, Quadratic Forms\, and their Applications in Coding
Theory''\, Contemporary Math.\, 2022\, available at: http://arxiv.org/abs
/2201.03295\n\n[3] A. Facchini\, C. A. Finocchiaro and G. Janelidze\, Abst
ractly constructed prime spectra\, Algebra universalis 83(1) (2022).\n\n[4
] A. Facchini\, F. de Giovanni and M. Trombetti\, Spectra of Groups\, Alge
bras Rep. Theory\, Online first articles published 5 June 2022.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Diniz (Universidade Federal de Campina Grande\, Brazil)
DTSTART:20221117T170000Z
DTEND:20221117T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/94
DESCRIPTION:Title: Gradings on block-triangular matrix algebras\nby Diogo
Diniz (Universidade Federal de Campina Grande\, Brazil) as part of LieJor
Online Seminar: Algebras\, representations\, and applications\n\n\nAbstrac
t\nUpper triangular\, and more generally\, block-triangular matrices\, are
rather important in Linear Algebra\, and also in Ring theory\, namely in
the theory of PI algebras. The group gradings on such algebras have been s
tudied extensively during the last decades. In 2007 A. Valenti and M. Zai
cev conjectured that every grading on these algebras is obtained from an e
lementary grading on a block-triangular matrix algebra and a division grad
ing on a matrix algebra. In this talk we present recent results on this pr
oblem.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Pchelintsev and Oleg Shashkov (Financial University under t
he Government of the Russian Federation\, Russia)
DTSTART:20220915T170000Z
DTEND:20220915T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/95
DESCRIPTION:Title: Simple right-alternative superalgebras\nby Sergey Pchel
intsev and Oleg Shashkov (Financial University under the Government of the
Russian Federation\, Russia) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nWe are going to talk ab
out what is known about simple right-alternative superalgebras at this tim
e. Right alternative superalgebras can be divided into two classes\, these
are unital and non-unital superalgebras. In the unital case\, the case of
simple superalgebras with a semisimple even part is completely described.
In the non-unital case\, we describe a class of simple superalgebras with
zero multiplication of the even part\, which we call the class of singula
r superalgebras. A scheme of the so-called extended double is given and it
is proved that every singular superalgebra is an extended double. The dim
ensions for which there are no singular superalgebras are indicated\, and
examples of singular superalgebras of all other dimensions are given.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Nikolov (Oxford University\, UK)
DTSTART:20221006T170000Z
DTEND:20221006T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/96
DESCRIPTION:Title: On conjugacy classes of profinite groups\nby Nikolay Ni
kolov (Oxford University\, UK) as part of LieJor Online Seminar: Algebras\
, representations\, and applications\n\n\nAbstract\nIt is well-known that
the number of conjugacy classes of a finite group G tends to infinity as t
he size of G tends to infinity. There is no such result for a general infi
nite group. In this talk I will discuss the situation when G is a profinit
e group and show that the number of conjugacy of G is then uncountable unl
ess G is finite. The proof depends on many classical results on finite gro
ups and in particular the classification of the finite simple groups. This
is joint work with Andrei Jaikin-Zapirain.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA\, Brazil)
DTSTART:20221013T170000Z
DTEND:20221013T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/97
DESCRIPTION:Title: Higher Fano manifolds\nby Carolina Araujo (IMPA\, Brazi
l) as part of LieJor Online Seminar: Algebras\, representations\, and appl
ications\n\n\nAbstract\nFano manifolds are complex projective manifolds ha
ving positive first Chern class. The positivity condition on the first Che
rn class has far reaching geometric and arithmetic implications. For insta
nce\, Fano manifolds are covered by rational curves\, and families of Fano
manifolds over one dimensional bases always admit holomorphic sections. I
n recent years\, there has been great effort towards defining suitable hig
her analogues of the Fano condition. Higher Fano manifolds are expected to
enjoy stronger versions of several of the nice properties of Fano manifol
ds. For instance\, they should be covered by higher dimensional rational v
arieties\, and families of higher Fano manifolds over higher dimensional b
ases should admit meromorphic sections (modulo Brauer obstruction). In thi
s talk\, I will discuss a possible notion of higher Fano manifolds in term
s of positivity of higher Chern characters\, and describe special geometri
c features of these manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Esteves (IMPA\, Brazil)
DTSTART:20221020T170000Z
DTEND:20221020T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/98
DESCRIPTION:Title: Quiver representations arising from degenerations of linear
series\nby Eduardo Esteves (IMPA\, Brazil) as part of LieJor Online S
eminar: Algebras\, representations\, and applications\n\n\nAbstract\nWe de
scribe all the schematic limits of divisors associated to any family of li
near series on any one-dimensional family of projective varieties degenera
ting to any connected reduced projective scheme X defined over any field\,
under the assumption that the total space of the family is regular along
X. More precisely\, the degenerating family gives rise to a special quiver
Q\, called a Z^n-quiver\, a special representation L of Q in the category
of line bundles over X\, called a maximal exact linked net\, and a specia
l subrepresentation V of the representation induced from L by taking globa
l sections\, called a pure exact finitely generated linked net. Given g=(Q
\, L\, V) satisfying these properties\, we prove that the quiver Grassmani
an G of subrepresentations of V of pure dimension 1\, called a linked proj
ective space\, is Cohen-Macaulay\, reduced and of pure dimension. Furtherm
ore\, we prove that there is a morphism from G to the Hilbert scheme of X
whose image parameterizes all the schematic limits of divisors along the d
egenerating family of linear series if g arises from one. Joint work with
Eduardo Vital and Renan Santos.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Bartholdi (Saarland University\, Germany)
DTSTART:20221027T170000Z
DTEND:20221027T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/99
DESCRIPTION:Title: Dimension series and homotopy groups of spheres\nby Lau
rent Bartholdi (Saarland University\, Germany) as part of LieJor Online Se
minar: Algebras\, representations\, and applications\n\n\nAbstract\nThe lo
wer central series of a group \\(G\\) is defined by \\(\\gamma_1=G\\) and
\\(\\gamma_n = [G\,\\gamma_{n-1}]\\). The "dimension series"\, introduced
by Magnus\, is defined using the group algebra over the integers: \\(\\del
ta_n = \\{g: g-1\\text{ belongs to the \\(n\\)-th power of the augmentatio
n ideal}\\}\\).
It has been\, for the last 80 years\, a fundamental
problem of group theory to relate these two series. One always has \\(\\d
elta_n\\ge\\gamma_n\\)\, and a conjecture by Magnus\, with false proofs by
Cohn\, Losey\, etc.\, claims that they coincide; but Rips constructed
an example with \\(\\delta_4/\\gamma_4\\) cyclic of order 2. On the positi
ve side\, Sjogren showed that \\(\\delta_n/\\gamma_n\\) is always a torsio
n group\, of exponent bounded by a function of \\(n\\). Furthermore\, it w
as believed (and falsely proven by Gupta) that only \\(2\\)-torsion may oc
cur.
In joint work with Roman Mikhailov\, we prove however that eve
ry torsion abelian group may occur as a quotient \\(\\delta_n/\\gamma_n\\)
; this proves that Sjogren's result is essentially optimal.
Even
more interestingly\, we show that this problem is intimately connected to
the homotopy groups \\(\\pi_n(S^m)\\) of spheres; more precisely\, the
quotient \\(\\delta_n/\\gamma_n\\) is related to the difference between h
omotopy and homology. We may explicitly produce \\(p\\)-torsion elements s
tarting from the order-\\(p\\) element in the homotopy group \\(\\pi_{2p}(
S^2)\\) due to Serre.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviane Ribeiro Tomaz da Silva (UFMG\, Brazil)
DTSTART:20221103T170000Z
DTEND:20221103T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/100
DESCRIPTION:Title: On the minimal varieties of PI *-superalgebras and the fac
torability of their T-ideals\nby Viviane Ribeiro Tomaz da Silva (UFMG\
, Brazil) as part of LieJor Online Seminar: Algebras\, representations\, a
nd applications\n\n\nAbstract\nIn this talk\, we deal with varieties of PI
-superalgebras with graded involution of finite basic rank over a field of
characteristic zero and we present some recent results concerning the min
imality of these varieties (of fixed *-graded exponent) and the factorabil
ity of their *-graded polynomial identities.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Klep (University of Ljubljana\, Slovenia)
DTSTART:20221110T170000Z
DTEND:20221110T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/101
DESCRIPTION:Title: Factorization of noncommutative polynomials and Nullstelle
nsätze for the free algebra\nby Igor Klep (University of Ljubljana
\, Slovenia) as part of LieJor Online Seminar: Algebras\, representations\
, and applications\n\n\nAbstract\nThe singularity set of a noncommutative
polynomial \\(f=f(x_1\,\\dots\,x_d)\\) is the graded set \\(Z(f)=(Z_n(f))_
n\\)\, where \\(Z_n(f)=\\{X \\in M_n^d: \\det f(X) = 0\\}.\\) Two main res
ults will be presented. Firstly\, irreducible factors of \\(f\\) are shown
to be in a natural bijective correspondence with irreducible components o
f \\(Z_n(f)\\) for every sufficiently large \\(n\\). In particular\, \\(f\
\) is irreducible if and only if \\(Z_n(f)\\) is eventually irreducible. S
econdly\, we give Nullstellensätze for noncommutative polynomials. For
instance\, given two noncommutative polynomials \\(f_1\,f_2\\)\, we have
\\(Z(f_1) \\subset Z(f_2)\\) if and only if each irreducible factor of \\(
f_1\\) is (up to stable associativity) an irreducible factor of \\(f_2\\).
Along the way an algorithm for factorization of noncommutative polynomial
s will be presented.
The talk is based on joint works with Jurij
Volčič and Bill Helton.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University\, USA)
DTSTART:20221208T170000Z
DTEND:20221208T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/102
DESCRIPTION:Title: An operadic approach to vertex algebras and Poisson vertex
algebras\nby Bojko Bakalov (North Carolina State University\, USA) as
part of LieJor Online Seminar: Algebras\, representations\, and applicati
ons\n\n\nAbstract\nI will start by reviewing the notions of vertex algebra
\, Poisson vertex algebra\, and Lie conformal algebra\, and their relation
s to each other. Then I will present a unified approach to all these algeb
ras as Lie algebras in certain pseudo-tensor categories\, or equivalently\
, as morphisms from the Lie operad to certain operads. As an application\,
I will introduce a cohomology theory of vertex algebras similarly to Lie
algebra cohomology\, and will show how it relates to the cohomology of Poi
sson vertex algebras and of Lie conformal algebras. The talk is based on j
oint work with Alberto De Sole\, Reimundo Heluani\, Victor Kac\, and Veron
ica Vignoli.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matyas Domokos (Renyu Institute of Mathematics\, Budapest\, Hungar
y)
DTSTART:20221124T170000Z
DTEND:20221124T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/103
DESCRIPTION:Title: Improvements of the Noether bound for polynomial invariant
s of finite groups\nby Matyas Domokos (Renyu Institute of Mathematics\
, Budapest\, Hungary) as part of LieJor Online Seminar: Algebras\, represe
ntations\, and applications\n\n\nAbstract\nGiven a field and a finite grou
p G\, the Noether number of G is defined as the minimal positive integer d
such that for any finite dimensional G-module V\, the algebra of G-invari
ant polynomial functions on V is generated by elements of degree at most d
. In the talk we shall survey results (obtained mostly together with Kálm
án Cziszter) on the Noether number of various finite groups.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Zalesski (UnB\, Brazil)
DTSTART:20221215T170000Z
DTEND:20221215T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/104
DESCRIPTION:Title: Combinatorial theory of pro-p groups\nby Pavel Zalessk
i (UnB\, Brazil) as part of LieJor Online Seminar: Algebras\, representati
ons\, and applications\n\n\nAbstract\nFree product with amalgamation and H
NN-extension are two main constructions of combinatorial group theory. I s
hall discuss these two constructions in the category of pro-\\(p\\) groups
\, presenting results on splittings of pro-\\(p\\) groups as an amalgamat
ed free pro-\\(p\\) product or a pro-\\(p\\) HNN-extension and relating th
em with pro-\\(p\\) version of Bass-Serre's theory of groups acting on tre
es. I shall also compare the pro-\\(p\\) results with similar results for
abstract groups.\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Yasumura (IME-USP\, Brazil)
DTSTART:20221201T170000Z
DTEND:20221201T180000Z
DTSTAMP:20260404T095031Z
UID:LieJor_Seminar/105
DESCRIPTION:Title: Group gradings on the infinite dimensional triangular alge
bra\nby Felipe Yasumura (IME-USP\, Brazil) as part of LieJor Online Se
minar: Algebras\, representations\, and applications\n\n\nAbstract\nIn the
last decades\, there has been an increasing interest in the classificatio
n of isomorphism classes of group gradings on a given algebra. We discuss
some difficulties concerning the study of group gradings on infinite-dimen
sional algebras. Then\, we present our results on the classification of th
e gradings on the infinite-dimensional triangular algebra. This is joint w
ork with Waldeck Schutzer (UFSCar).\n
LOCATION:https://stable.researchseminars.org/talk/LieJor_Seminar/105/
END:VEVENT
END:VCALENDAR