BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Albert Schwarz (UC Davis)
DTSTART:20200827T170000Z
DTEND:20200827T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/1
DESCRIPTION:Title: Some questions on Jordan algebras inspired by quantum theory\nb
y Albert Schwarz (UC Davis) as part of LieJor Online Seminar: Algebras\, r
epresentations\, and applications\n\n\nAbstract\nOne can formulate quantum
theory taking as a starting point a convex set (the set of states) or a c
onvex cone (the set of non-normalized states.) Jordan algebras are closely
related to homogeneous cones\, therefore they appear naturally in this fo
rmulation. There exists a conjecture that superstring can be formulated in
terms of exceptional Jordan algebras. In my purely mathematical talk I'll
formulate some results and conjectures on Jordan algebras coming from the
se ideas.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Mostovoy (SINVESTAV)
DTSTART:20200903T170000Z
DTEND:20200903T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/2
DESCRIPTION:Title: The Chevalley-Eilenberg complex for Leibniz and for Sabinin algebra
s\nby Jacob Mostovoy (SINVESTAV) as part of LieJor Online Seminar: Alg
ebras\, representations\, and applications\n\n\nAbstract\nI will show how
to generalize the Chevalley-Eilenberg complex of a Lie algebra to Sabinin
algebras and to Leibniz algebras. I will also show how Leibniz algebras ca
n be interpreted as a very basic kind of DG Lie algebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20200910T170000Z
DTEND:20200910T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/3
DESCRIPTION:Title: The singular support of the Ising model\nby Reimundo Heluani (I
MPA) as part of LieJor Online Seminar: Algebras\, representations\, and ap
plications\n\n\nAbstract\nWe prove three new q-series identities of the Ro
gers-Ramanujan-Slater type. We find a PBW basis for the Ising model as a c
onsequence of one of these identities. If time permits it will be shown th
at the singular support of the Ising model is a hyper-surface (in the diff
erential 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 at https
://arxiv.org/abs/2005.10769\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Makar-Limanov (Wayne State University)
DTSTART:20200917T170000Z
DTEND:20200917T180000Z
DTSTAMP:20260422T213011Z
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://researchseminars.org/talk/LieJor_Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Molev (University of Sidney)
DTSTART:20201001T130000Z
DTEND:20201001T140000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/5
DESCRIPTION:Title: Symmetrization map\, Casimir elements and Sugawara operators\nb
y Alexander Molev (University of Sidney) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nThe canonica
l symmetrization map is a g-module isomorphism between the symmetric algeb
ra S(g) of a finite-dimensional Lie algebra g and its universal enveloping
algebra U(g). This implies that the images of g-invariants in S(g) are Ca
simir elements. For each simple Lie algebra g of classical type we conside
r basic g-invariants arising from the characteristic polynomial of the mat
rix of generators. We calculate the Harish-Chandra images of the correspon
ding Casimir elements. By using counterparts of the symmetric algebra inva
riants for the associated affine Kac-Moody algebras we obtain new formulas
for generators of the centers of the affine vertex algebras at the critic
al level. Their Harish-Chandra images are elements of classical W-algebras
which we produce in an explicit form.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Elduque (Universidad de Zaragoza)
DTSTART:20201008T170000Z
DTEND:20201008T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/6
DESCRIPTION:Title: Graded-simple algebras and twisted loop algebras\nby Alberto El
duque (Universidad de Zaragoza) as part of LieJor Online Seminar: Algebras
\, representations\, and applications\n\n\nAbstract\nThe loop algebra cons
truction by Allison\, Berman\, Faulkner\, and Pianzola (2008)\, describes
graded-central-simple algebras with "split centroid" in terms of central s
imple algebras graded by a quotient of the original grading group. Particu
lar versions of this result were considered by several authors.\n\nIn this
talk it will be shown how the restriction on the centroid can be removed\
, at the expense of allowing some deformations (cocycle twists) of the loo
p algebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Grantcharov (University of Texas Arlington)
DTSTART:20201015T170000Z
DTEND:20201015T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/7
DESCRIPTION:Title: Quantized enveloping superalgebra of type P\nby Dimitar Grantch
arov (University of Texas Arlington) as part of LieJor Online Seminar: Alg
ebras\, representations\, and applications\n\n\nAbstract\nWe will introduc
e a new quantized enveloping superalgebra corresponding to the periplectic
Lie superalgebra p(n). This quantized enveloping superalgebra is a quanti
zation of a Lie bisuperalgebra structure on p(n). Furthermore\, we will de
fine the periplectic q-Brauer algebra and see that it admits natural centr
alizer properties. This is joint work with N. Guay and S. Ahmed.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Kharlampovich (Hunter College CUNY)
DTSTART:20201029T170000Z
DTEND:20201029T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/8
DESCRIPTION:Title: Frasse limits of limit groups\nby Olga Kharlampovich (Hunter Co
llege CUNY) as part of LieJor Online Seminar: Algebras\, representations\,
and applications\n\n\nAbstract\nWe modify the notion of a Fraïssé class
and show that various interesting classes of groups\, notably the class o
f nonabelian limit groups and the class of finitely generated elementary f
ree groups\, admit Fraïssé limits. We will also discuss countable elemen
tary free groups. The talk is based on joint results with A. Miasnikov\, C
. Natoli and R. Sklinos.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Mikhalev (Lomonosov Moscow State University)
DTSTART:20201112T160000Z
DTEND:20201112T170000Z
DTSTAMP:20260422T213011Z
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://researchseminars.org/talk/LieJor_Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Bulgarian Academy of Sciences)
DTSTART:20201217T170000Z
DTEND:20201217T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/10
DESCRIPTION:Title: From a Diophantine transport problem from 2016 and its possible so
lution from 1903 to classical problems in algebra\nby Vesselin Drensky
(Bulgarian Academy of Sciences) as part of LieJor Online Seminar: Algebra
s\, representations\, and applications\n\n\nAbstract\nMotivated by a recen
t Diophantine transport problem about how to transport profitably a group
of persons or objects\, we survey classical facts about solving systems of
linear Diophantine equations and inequalities in nonnegative integers. We
emphasize on the method of Elliott from 1903 and its further development
by MacMahon in his “$\\Omega$-Calculus” or Partition Analysis. Then we
show how this approach can be used to solve problems in classical and non
commutative invariant theory and theory of algebras with polynomial identi
ties. The obtained results are due to a big team of mathematicians in Bulg
aria\, Italy\, Turkey and Hungary. The talk is a joint project with Silvia
Boumova.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Louisiana State University)
DTSTART:20201001T150000Z
DTEND:20201001T160000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/11
DESCRIPTION:Title: Quantum cluster algebras at roots of unity and discriminants\n
by Milen Yakimov (Louisiana State University) as part of LieJor Online Sem
inar: Algebras\, representations\, and applications\n\n\nAbstract\nCluster
Algebra were invented by Fomin and Zelevinsky twenty years ago. Since the
n they have played an important role in a number of settings in combinator
ics\, geometry\, representation theory and topology. We will introduce a n
otion of root of unity quantum cluster algebras which are PI algebras\, an
d will show that they have large canonical central subalgebras isomorphic
to the original cluster algebras. These are far reaching generalizations o
f the De Concini-Kac-Procesi central subalgebras that appear in the study
of the irreducible representations of big quantum groups. We will describe
a general theorem computing the discriminants of these algebras. In a spe
cial situation it yields a formula for the discriminants of the quantum un
ipotent cells at roots of unity associated to all symmetrizable Kac-Moody
algebras. This is a joint work with Bach Nguyen (Xavier Univ) and Kurt Tra
mpel (Univ Notre Dame).\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Premet (University of Manchester)
DTSTART:20200924T170000Z
DTEND:20200924T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/12
DESCRIPTION:Title: Modular representations of Lie algebras and Humphreys' Conjecture<
/a>\nby Alexander Premet (University of Manchester) as part of LieJor Onli
ne Seminar: Algebras\, representations\, and applications\n\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Libedinsky (Universidad de Chile)
DTSTART:20201105T170000Z
DTEND:20201105T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/13
DESCRIPTION:Title: On Kazhdan-Lusztig theory for affine Weyl groups\nby Nicolas L
ibedinsky (Universidad de Chile) as part of LieJor Online Seminar: Algebra
s\, representations\, and applications\n\n\nAbstract\nKazhdan-Lusztig poly
nomials are a big mystery. On a recent work with Leonardo Patimo (followin
g 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 new resul
ts in this direction and what we believe that is doable. Another part of t
his project is to produce an approach towards the following question: for
a given element in an affine Weyl group\, what are the prime numbers p suc
h that the p-canonical basis is different from the canonical basis? This i
s a joint project with Leonardo Patimo and David Plaza.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claude Cibils (Université de Montpellier)
DTSTART:20201210T170000Z
DTEND:20201210T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/14
DESCRIPTION:Title: Controlling the global dimension\nby Claude Cibils (Universit
é de Montpellier) as part of LieJor Online Seminar: Algebras\, representa
tions\, and applications\n\n\nAbstract\nThe global dimension of an associa
tive algebra A over a a field is a measure of the complexity of its repres
entations. It is 0 if A is a matrix algebra. It is 1 if A is a path algebr
as of quivers without directed cycles. It is infinite if A is the algebra
of dual numbers.\n\nI will give a brief introduction to Hochschild homolog
y (1945)\, in order to explain Han's conjecture (2006): for finite-dimensi
onal algebras\, the Hochschild homology should control the finiteness of t
he global dimension.\n\nNext\, I will present some progress made in showin
g the Han's conjecture\, using the relative version of Hochschild homology
(1956) with respect to a subalgebra B. This theory was little used until
recently. Now we have a Jacobi-Zariski long nearly exact sequence which re
lates the usual and relative versions of Hochschild homology. Its gap to b
e exact is approximated by a spectral sequence which has Tor functors in i
ts 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 close
d by bounded extensions of algebras. These results have been obtained in j
oint work with M. Lanzilotta\, E. N. Marcos and A. Solotar.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Nakano (University of Georgia)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/15
DESCRIPTION:Title: A new Lie theory for classical Lie superalgebras\nby Daniel Na
kano (University of Georgia) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nIn 1977\, Kac classified
simple Lie superalgebras over \\({\\mathbb C}\\) and showed they play 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 treat th
e structure and representation theory for these groups and Lie algebras. H
istorically\, much of the work for simple Lie superalgebras has involved d
ealing with these objects using a case by case analysis.
Fifteen
years ago\, Boe\, Kujawa and the speaker introduced the concept of detecti
ng subalgebras for classical Lie superalgebras. These algebras were constr
ucted by using ideas from geometric invariant theory. More recently\, D. G
rantcharov\, N. Grantcharov\, Wu and the speaker introduced the concept of
a BBW parabolic subalgebra. Given a Lie superalgebra \\({\\mathfrak g}\\)
\, one has a triangular decomposition \\({\\mathfrak g}={\\mathfrak n}^{-}
\\oplus {\\mathfrak f} \\oplus {\\mathfrak n}^{+}\\) with \\({\\mathfrak b
}={\\mathfrak f}\\oplus {\\mathfrak n}^{-}\\) where \\({\\mathfrak f}\\) i
s a detecting subalgebra and \\({\\mathfrak b}\\) is a BBW parabolic subal
gebra. This holds for all classical "simple" Lie superalgebras\, and one c
an view \\({\\mathfrak f}\\) as an analog of the maximal torus\, and \\({\
\mathfrak b}\\) like a Borel subalgebra. This setting also provide a usefu
l method to define semisimple elements and nilpotent elements\, and to com
pute various sheaf cohomology groups \\(R^{\\bullet}\\text{ind}_{B}^{G} (-
)\\).
The goal of my talk is to provide a survey of the main ide
as of this new theory and to give indications of the interconnections with
in the various parts of this topic. I will also indicate how this treatmen
t can further unify the study of the representation theory of classical Li
e superalgebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Zaicev (Lomonosov Moscow State University)
DTSTART:20201022T170000Z
DTEND:20201022T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/16
DESCRIPTION:Title: Polynomial identities: anomalies of codimension growth\nby Mik
hail Zaicev (Lomonosov Moscow State University) as part of LieJor Online S
eminar: Algebras\, representations\, and applications\n\n\nAbstract\nMikha
il Zaicev (Lomonosov Moscow State University\, Russia): Polynomial identi
ties: anomalies of codimension growth. Polynomi
al 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 associat
ed with polynomial identities of algebras over a field of characteristic z
ero. Given an algebra \\(A\\)\, one can construct a sequence of non-negati
ve integers \\({c_n(A)}\, n=1\,2\, \\ldots \\)\, called the codimensions o
f \\(A\\)\, which is an important numerical characteristic of identical re
lations of \\(A\\). In present talk we discuss asymptotic behavior of codi
mension sequence in different classes of algebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Iyudu (University of Edinburgh)
DTSTART:20201119T170000Z
DTEND:20201119T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/17
DESCRIPTION:Title: On the proof of the Kontsevich conjecture on noncommutative birati
onal transformations\nby Natalia Iyudu (University of Edinburgh) as pa
rt of LieJor Online Seminar: Algebras\, representations\, and applications
\n\n\nAbstract\nI will talk about our proof (arxiv 1305.1965\, Duke math J
.) of the Kontsevich conjecture (1996) on noncommutative birational transf
ormations. It deals with difficulties arising out of the fact that there a
re no canonical form for noncommutative rational expressions. Miraculous i
dentities proved supposedly reflect some kind of noncommutative group acti
ons.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eli Aljadeff (Technion-Israel Institute of Technology)
DTSTART:20201126T170000Z
DTEND:20201126T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/18
DESCRIPTION:Title: PI theory\, generic objects and group gradings\nby Eli Aljadef
f (Technion-Israel Institute of Technology) as part of LieJor Online Semin
ar: Algebras\, representations\, and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agata Smoktunowicz (University of Edinburgh)
DTSTART:20210225T170000Z
DTEND:20210225T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/19
DESCRIPTION:Title: Some questions related to nilpotent rings and braces\nby Agata
Smoktunowicz (University of Edinburgh) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nIn around 200
5\, 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 application in
other research areas. This talk will review these applications.
Definition. A set \\(A\\) with binary operations of addition \\(+\
\)\, and multiplication \\(\\circ\\) is a brace if \\((A\, +)\\) is an abe
lian 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 from thi
s definition that every nilpotent ring with the usual addition and with mu
ltiplication \\(a \\circ b = ab + a + b\\) is a brace.
Braces h
ave been shown to be equivalent to several concepts in group theory such a
s groups with bijective 1-cocycles and regular subgroups of the holomorph
of abelian groups. In algebraic number theory there is a correspondence be
tween braces and Hopf-Galois extensions of abelian type first observed by
David Bachiller. There is also connection between R-braces and pre-Lie alg
ebras discovered by Wolfgang Rump in 2014. One generator braces have been
shown to describe indecomposable\, involutive solutions of the Yang-Baxter
equation.
On the other hand\, Anastasia Doikou and Robert West
on have recently discovered some fascinating connections between braces an
d quantum integrable systems. In particular\, to find solutions of the set
-theoretic reflection equation it is needed to solve problems on some poly
nomial identities in nilpotent rings. Because previously the theory of pol
ynomial identities was mainly developed for prime rings\, and for the refl
ection equation we only consider nilpotent rings\, there are no known meth
ods for solving such problems. We will mention some open problems on polyn
omial identities in nilpotent rings which appear in this situation.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (Université de Strasbourg)
DTSTART:20210304T170000Z
DTEND:20210304T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/20
DESCRIPTION:Title: Diamond Lemma and the Maurer-Cartan equation\nby Vladimir Dots
enko (Université de Strasbourg) as part of LieJor Online Seminar: Algebra
s\, representations\, and applications\n\n\nAbstract\nI shall outline a ne
w approach to the Composition-Diamond Lemma for rewriting systems / Gr&oum
lbner-Shirshov bases; more specifically\, I shall explain how the Maure
r-Cartan equation in the tangent complex of a monomial algebra leads to ma
ny different versions of the Composition-Diamond Lemma\, one for each repr
esentative of the tangent complex arising from a multigraded resolution of
such algebra. This is joint work with Pedro Tamaroff.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandr Zubkov (UAEU (United Arab Emirates))
DTSTART:20210311T170000Z
DTEND:20210311T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/21
DESCRIPTION:Title: Harish-Chandra pairs and group superschemes\nby Alexandr Zubko
v (UAEU (United Arab Emirates)) as part of LieJor Online Seminar: Algebras
\, representations\, and applications\n\n\nAbstract\nThe purpose of my tal
k is to discuss the following results recently obtained in collaboration w
ith A.Masuoka (Tsukuba University\, Japan). First\, we prove that a certai
n category of Harish-Chandra pairs is equivalent to the category of (not n
ecessary affine) locally algebraic group superschemes. Using this fundamen
tal equivalence we superize the famous Barsotti-Chevalley theorem and prov
e that the sheaf quotient of an algebraic group superscheme over its group
super-subscheme is again a superscheme of finite type. I will also formul
ate some open problems whose solving would bring significant progress in t
he supergroup theory.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (The Weizmann Institute of Science\, Israel)
DTSTART:20210318T170000Z
DTEND:20210318T180000Z
DTSTAMP:20260422T213011Z
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 Online Sem
inar: Algebras\, representations\, and applications\n\n\nAbstract\nThe Dul
fo-Serganova functors DS are tensor functors relating representations of d
ifferent Lie superalgebras. In this talk I will consider the behaviour of
various invariants\, such as the defect\, the dual Coxeter number\, the at
ypicality and the cores\, under the DS-functor. I will introduce a notion
of depth playing the role of defect for algebras and atypicality for modul
es. I will mainly concentrate on examples of symmetrizable Kac-Moody and Q
-type superalgebras. The talk is based on arXiv:2010.05721\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apoorva Khare (Indian Institute of Science)
DTSTART:20210325T170000Z
DTEND:20210325T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/23
DESCRIPTION:Title: Polymath14: Groups with norms\nby Apoorva Khare (Indian Instit
ute of Science) as part of LieJor Online Seminar: Algebras\, representatio
ns\, and applications\n\n\nAbstract\nConsider the following three properti
es of a general group \\(G\\):
Algebra: \\(G\\) is abelian and
torsion-free.
Analysis: \\(G\\) is a metric space that admits a "nor
m"\, namely\, a translation-invariant metric \\(d(.\,.)\\) satisfying: \\(
d(1\,g^n) = |n| d(1\,g)\\) for all \\(g \\in G\\) and integers \\(n\\). Geometry: \\(G\\) admits a length function with "saturated" subadditiv
ity 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 t
urn out to be equivalent (and also to \\(G\\) being isometrically and addi
tively embedded in a Banach space\, hence inheriting its norm). The nontri
vial implication amounts to saying that there does not exist a non-abelian
group with a "norm". We will discuss motivations from analysis\, probabil
ity\, and geometry; then the proof of the above equivalences; and fi
nally\, the logistics of how the problem was solved\, via a PolyMath proje
ct that began on a blog post of Terence Tao.
(Joint - as D.H.J
. PolyMath - with Tobias Fritz\, Siddhartha Gadgil\, Pace Nielsen\, Lior S
ilberman\, and Terence Tao.)\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/24
DESCRIPTION:Title: Quantum Borcherds-Bozec algebras and abstract crystals\nby Kan
g Seok-Jin (Korea Research Institute of Arts and Mathematics\, South Korea
) as part of LieJor Online Seminar: Algebras\, representations\, and appli
cations\n\n\nAbstract\nIn this talk\, we will discuss the basic properties
of quantum Borcherds-Bozec algebras and their integrable representations.
We also give a brief description of the theory of abstract crystals for q
uantum Borcherds-Bozec algebras and their applications.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Mukhin (IUPUI School of Science\, USA)
DTSTART:20210408T170000Z
DTEND:20210408T180000Z
DTSTAMP:20260422T213011Z
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 Online Sem
inar: Algebras\, representations\, and applications\n\n\nAbstract\nWe will
explain combinatorics of various partitions arising in the representation
theory of quantum toroidal algebras associated to Lie superalgebra gl(m|n
). Apart from being interesting in its own right\, this combinatorics is e
xpected to be related to crystal bases\, fixed points of the moduli spaces
of BPS states\, equivariant K-theory of moduli spaces of maps\, and other
things. This talk is based on a joint project with Luan Bezerra.\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/26
DESCRIPTION:Title: Some aspects of the free nonassociative algebra\nby José
María Pérez Izquierdo (Universidad de La Rioja\, Spain) as pa
rt of LieJor Online Seminar: Algebras\, representations\, and applications
\n\n\nAbstract\nThe free nonassociative algebra provides a simple combinat
orial context to extend some constructions from the associative setting. I
n this talk\, based on joint work with J. Mostovoy and I. P. Shestakov\, I
will briefly discuss three of them related to nonassociative Lie theory:
the embedding of the free loop as nonassociative formal power series\, a n
onassociative extension of the Baker-Campbell-Hausdorff formula and a nona
ssociative version of Solomon's descent algebra.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Belolipetsky (IMPA\, Brazil)
DTSTART:20210422T180000Z
DTEND:20210422T190000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/27
DESCRIPTION:Title: Growth of lattices in semisimple Lie groups\nby Mikhail Beloli
petsky (IMPA\, Brazil) as part of LieJor Online Seminar: Algebras\, repres
entations\, and applications\n\n\nAbstract\nA discrete subgroup \\(G\\) of
a Lie group \\(H\\) is called a lattice if the quotient space \\(H/G\\) h
as finite volume. By a classical theorem of Bieberbach we know that the gr
oup of isometries of an \\(n\\)-dimensional Euclidean space has only finit
ely many different types of lattices. The situation is different for the s
emisimple Lie groups \\(H\\). Here the total number of lattices is infinit
e and we can study its growth rate with respect to the covolume. This topi
c has been a subject of our joint work with A. Lubotzky for a number of ye
ars. In the talk I will discuss our work and some other more recent relate
d results.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Shpectorov (University of Birmingham\, UK)
DTSTART:20210429T170000Z
DTEND:20210429T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/28
DESCRIPTION:Title: 2-generated algebras of Monster type\nby Sergey Shpectorov (Un
iversity of Birmingham\, UK) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nThe class of non-associa
tive axial algebras was introduced in 2015 as a broad generalisation of Ma
jorana algebras of Ivanov that were modelled after the properties of the G
riess algebra\, the algebra whose automorphism group is the Monster sporad
ic simple group. Sakuma's theorem classifies 2-generated Majorana algebras
\, which in axial terms correspond to algebras of Monster type (1/4\,1/32)
. The quest to classify all 2-generated algebras of arbitrary Monster type
\\((\\alpha\,\\beta)\\) was started by Rehren who proved an upper bound o
n the dimension and generalised the Norton-Sakuma algebras to arbitrary \\
((\\alpha\,\\beta)\\). Recently\, new results emerged from the work of Fra
nchi\, Mainardis and the speaker\, and independently\, of Yabe\, who class
ified symmetric 2-generated algebras of Monster type. Several new classes
of algebras have been found.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Rozhkovskaya (Kansas State University\, USA)
DTSTART:20210506T170000Z
DTEND:20210506T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/29
DESCRIPTION:Title: Generating functions of polynomial tau-functions of the soliton hi
erarchies\nby Natasha Rozhkovskaya (Kansas State University\, USA) as
part of LieJor Online Seminar: Algebras\, representations\, and applicatio
ns\n\n\nAbstract\nThe Kademtsev-Petviashvily (KP) equation is a famous evo
lution equation with soliton solutions. It was discovered by M.Sato and th
e Kyoto school that the KP equation can be regarded as a part of a countab
le system of compatible evolution equations\, which is called today the KP
hierarchy. The observation allowed the researchers to discover many new e
xamples of soliton type hierarchies and to study them with methods of math
ematical physics\, algebraic geometry and representation theory. In the ta
lk we will describe the explicit construction of polynomial tau-functions
of the KP\, BKP hierarchies through their generating functions. The method
uses the tools of representation theory and properties of symmetric funct
ions. The talk is based on the joint work with V. G. Kac and J. van de Leu
r.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa\, Canada)
DTSTART:20210513T170000Z
DTEND:20210513T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/30
DESCRIPTION:Title: Affine Hecke algebras and the elliptic Hall algebra\nby Alista
ir Savage (University of Ottawa\, Canada) as part of LieJor Online Seminar
: Algebras\, representations\, and applications\n\n\nAbstract\nThe ellipti
c Hall algebra has appeared in many different contexts in representation t
heory and geometry under different names. We will explain how this algebra
is categorified by the quantum Heisenberg category\, which is a diagramma
tic category modelled on affine Hecke algebras. This categorification can
be used to construct large families of representations for the elliptic Ha
ll algebra.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farkhod Eshmatov (Academy of Science of Uzbekistan\, Uzbekistan)
DTSTART:20210520T170000Z
DTEND:20210520T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/31
DESCRIPTION:Title: On transitive action on quiver varieties\nby Farkhod Eshmatov
(Academy of Science of Uzbekistan\, Uzbekistan) as part of LieJor Online S
eminar: Algebras\, representations\, and applications\n\n\nAbstract\nThe C
alogero-Moser space \\({\\mathcal C}_n\\) is the space of conjugacy classe
s 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\, repr
esentation theory and integrable systems. A well-known result of Berest an
d Wilson states that the natural action of the affine Cremona group \\(GA_
2\\) on \\({\\mathcal C}_n\\) is transitive. In this talk we will give a q
uiver generalization of this statement and discuss some applications.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kleshchev (University of Oregon\, USA)
DTSTART:20210527T170000Z
DTEND:20210527T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/32
DESCRIPTION:Title: Irreducible restrictions from symmetric groups to subgroups\nb
y Alexander Kleshchev (University of Oregon\, USA) as part of LieJor Onlin
e Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nWe
motivate\, discuss history of\, and present a solution to the following p
roblem: describe pairs \\((G\,V)\\) where \\(V\\) is an irreducible repres
entation of the symmetric group \\(S_n\\) of dimension \\(>1\\) and \\(G\\
) is a subgroup of \\(S_n\\) such that the restriction of \\(V\\) to \\(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 with Pham
Huu Tiep and Lucia Morotti.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Bavula (The University of Sheffield\, UK)
DTSTART:20210401T170000Z
DTEND:20210401T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/33
DESCRIPTION:Title: The global dimension of the algebras of polynomial integro-differe
ntial operators and the Jacobian algebras\nby Vladimir Bavula (The Uni
versity of Sheffield\, UK) as part of LieJor Online Seminar: Algebras\, re
presentations\, and applications\n\n\nAbstract\nWe review some old and rec
ent results about the algebras of polynomial integro-differential operator
s and the Jacobian algebras.\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/34
DESCRIPTION:Title: Local and 2-local derivations and automorphisms of Octonian algebr
as\nby Shavkat Ayupov (V.I.Romanovskiy Institute of Mathematics Uzbeki
stan Academy of Sciences) as part of LieJor Online Seminar: Algebras\, rep
resentations\, and applications\n\n\nAbstract\nThe talk is devoted to desc
ription of local and 2-local derivations (respectively\, automorphisms) on
octonian algebras over fields with zero characteristics. We shall give a
general form of local derivations on the real octonion algebra \\(O(\\math
bb{R})\\). This description implies that the space of all local derivation
s on \\(O(\\mathbb{R})\\) when equipped with Lie bracket is isomorphic 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 octonion
algebra \\(O(F)\\) over an algebraically closed field \\(F\\) and prove th
at every 2-local derivation on \\(O(F)\\) is a derivation. Further\, we ap
ply these results to problems for the simple 7-dimensional Malcev algebra.
As a corollary we obtain that the real octonion algebra \\(O(\\mathbb{R})
\\) and Malcev algebra \\(M_7(R)\\) are simple non associative algebras wh
ich admit pure local derivations\, that is\, local derivations which are n
ot derivation. Further\, we shall give a general form of local automorphis
ms on the octonion algebra \\(O(F)\\) over a field \\(F\\). This descripti
on implies that the group of all local automorphisms on \\(O(F)\\) is isom
orphic to the group \\(O_7(F)\\) of all orthogonal \\(7 \\times 7\\)-matri
ces over F. We also consider 2-local automorphisms on the octonion algebra
\\(O(F)\\) over an algebraically closed field \\(F\\) and prove that ever
y 2-local automorphism on \\(O(F)\\) is an automorphism. As a corollary we
obtain descriptions of local and 2-local automorphisms of seven dimension
al simple Malcev algebra.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (IME-USP\, Brazil)
DTSTART:20210603T170000Z
DTEND:20210603T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/35
DESCRIPTION:Title: Infinite-dimensional representations of Lie algebras\nby Vyach
eslav Futorny (IME-USP\, Brazil) as part of LieJor Online Seminar: Algebra
s\, representations\, and applications\n\n\nAbstract\nWe will discuss 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://researchseminars.org/talk/LieJor_Seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Pantev (University of Pennsylvania\, USA)
DTSTART:20210610T170000Z
DTEND:20210610T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/36
DESCRIPTION:Title: Geometry and topology of wild character varieties\nby Tony Pan
tev (University of Pennsylvania\, USA) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nWild character
varieties parametrize monodromy representations of flat meromorphic conne
ctions on compact Riemann surfaces. They are classical objects with remark
able geometric and topological properties. \n\nI will recall how intrinsic
geometric structures resolve singularities of wild character varieties an
d will show that known algebraic symplectic structures extend naturally to
the resolutions. This is based on a new universal method for producing sy
mplectic structures which is a joint work with Arinkin and Toen. Time perm
itting I may also describe recent joint works with Chuang\, Diaconescu\, D
onagi\, and Nawata which extract cohomological invariants of wild characte
r varieties from enumerative Calabi-Yau geometry and refined Chern-Simons
invariants of torus knots.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geordie Williamson (University of Sydney\, Australia)
DTSTART:20210617T200000Z
DTEND:20210617T210000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/37
DESCRIPTION:Title: Spectra in representation theory\nby Geordie Williamson (Unive
rsity of Sydney\, Australia) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nIn geometric representat
ion theory cohomology\, intersection cohomology and constructible sheaves
show up everywhere. This might seem strange to an algebraic topologist\, w
ho might ask: why this emphasis on cohomology\, when there are so many oth
er interesting cohomology theories (like K-theory\, elliptic cohomology\,
complex cobordism\, ...) out there? They might also ask: is there somethin
g like "intersection K-theory"\, or "intersection complex cobordism"? This
is something I've often wondered about. I will describe work in progress
with Ben Elias\, where we use Soergel bimodules to investigate what KU-mod
ules look like on the affine Grassmannian. We have checked by hand that in
types A1\, A2 and B2\, one gets something roughly resembling the quantum
group. Speaking very roughly\, the intersection K-theory of Schubert varie
ties in the affine Grassmannian should recover the irreducible representat
ions of the quantum group. Inspirations for this work include a strange Ca
rtan matrix discovered by Ben Elias\, and work of Cautis-Kamnitzer.\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/38
DESCRIPTION:Title: Embedding theorems for solvable groups\nby Vitaly A. Roman'kov
(Sobolev Institute of Mathematics RAS\, Omsk Branch\, Omsk\, Russia) as p
art of LieJor Online Seminar: Algebras\, representations\, and application
s\n\n\nAbstract\nIn this talk\, we present a series of results on group em
beddings in groups with a small number of generators. We show that each fi
nitely 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 variety of
abelian groups. If \\(G\\) is a finite group\, then \\(H\\) can also be f
ound as a finite group. It follows\, that any finitely generated (finite)
solvable group \\(G\\) of the derived length \\(l\\) can be embedded in a
4-generated (finite) solvable group \\(H\\) of length \\(l+1\\). Thus\, we
answer the question of V. H. Mikaelian and A.Yu. Olshanskii. It is also s
hown that any countable group \\(G\\) in M\, such that the abelianization
\\(G_{ab}\\) is a free abelian group\, is embeddable in a 2-generated grou
p \\(H\\) in MA.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry V. Artamonov (Lomonosov State University\, Moscow)
DTSTART:20210701T170000Z
DTEND:20210701T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/39
DESCRIPTION:Title: \\(3j\\)-symbols for the algebra \\(gl_3\\)\nby Dmitry V. Arta
monov (Lomonosov State University\, Moscow) as part of LieJor Online Semin
ar: Algebras\, representations\, and applications\n\n\nAbstract\nThe probl
em of caculation of Clebsh-Gordan coefficients for a tensor product of two
irreducible representations of the Lie algebra \\(gl_2\\) is well-investi
gated. It's solution plays an importan role in quantum mechanics. Analogou
s problem for the algebra \\(gl_3\\) is also improtant (in the theory of q
uarks)\, but it it much l more difficult. In some sence it was solved in t
he 60-s in a series of papers by Biedenharn\, Louck\, Baird. But their
solution is very cumbersome and not explicit. Thus the problem of findind
of an explicit and simple formula for a Clebsh-Gordan coefficient remained
unsolved.
In the talk an explicit and simple formula for a Cleb
sh-Gordan coefficient for the algebra \\(gl_3\\) will be presented. The a
nswer will be given as a value at \\(1\\) of some \\(A\\)-hypergeometric f
unction.
As a byproduct I shall give an explicit description of i
nvariants in triple tensor product and a projection on the corresponding
trivial representation.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kotchetov (Memorial University of Newfoundland\, Canada)
DTSTART:20210708T170000Z
DTEND:20210708T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/40
DESCRIPTION:Title: Fine gradings on classical simple Lie algebras\nby Mikhail Kot
chetov (Memorial University of Newfoundland\, Canada) as part of LieJor On
line Seminar: Algebras\, representations\, and applications\n\n\nAbstract\
nGradings by abelian groups have played an important role in the theory of
Lie algebras since its beginning: the best known example is the root spac
e decomposition of a semisimple complex Lie algebra\, which is a grading b
y a free abelian group (the root lattice). Involutive automorphisms or\, e
quivalently\, gradings by the cyclic group of order 2\, appear in the clas
sification of real forms of these Lie algebras. Gradings by all cyclic gro
ups were classified by V. Kac in the late 1960s and applied to the study o
f symmetric spaces and affine Kac-Moody Lie algebras.\n\nIn the past two d
ecades there has been considerable interest in classifying gradings by arb
itrary groups on algebras of different varieties including associative\, L
ie and Jordan. Of particular importance are the so-called fine gradings (t
hat is\, those that do not admit a proper refinement)\, because any gradin
g on a finite-dimensional algebra can be obtained from them via a group ho
momorphism\, although not in a unique way. If the ground field is algebrai
cally closed and of characteristic 0\, then the classification of fine abe
lian group gradings on an algebra (up to equivalence) is the same as the c
lassification of maximal quasitori in the algebraic group of automorphisms
(up to conjugation). Such a classification is now known for all finite-di
mensional simple complex Lie algebras.\n\nIn this talk I will review the a
bove mentioned classification and present a recent joint work with A. Eldu
que and A. Rodrigo-Escudero in which we classify fine gradings on classica
l simple real Lie algebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Lubotzky (Hebrew University\, Jerusalem\, Israel)
DTSTART:20210715T170000Z
DTEND:20210715T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/41
DESCRIPTION:Title: First order rigidity of high-rank arithmetic groups\nby Alex L
ubotzky (Hebrew University\, Jerusalem\, Israel) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Berest (Cornell University\, USA)
DTSTART:20210722T170000Z
DTEND:20210722T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/42
DESCRIPTION:Title: Spaces of quasi-invariants and homotopy Lie groups\nby Yuri Be
rest (Cornell University\, USA) as part of LieJor Online Seminar: Algebras
\, representations\, and applications\n\n\nAbstract\nQuasi-invariants are
natural algebraic generalizations of classical invariant polynomials of fi
nite reflection groups. They first appeared in mathematical physics --- in
the work of O. Chalykh and A. Veselov on quantum integrable systems --- i
n the early 1990s\, and since then have found many interesting application
s in other areas: most notably\, representation theory\, algebraic geometr
y and combinatorics.\n\nIn this talk\, I will explain how the algebras of
quasi-invariants arise in topology: as cohomology rings of certain spaces
naturally attached to compact connected Lie groups. Our main result is a g
eneralization of a well-known theorem of A. Borel that realizes the algebr
a of classical invariant polynomials of a Weyl group W(G) as the cohomolog
y ring of the classifying space BG of the corresponding Lie group G. Perha
ps most interesting here is the fact that our construction of spaces of qu
asi-invariants is purely homotopy-theoretic. It can therefore be extended
to some non-Coxeter (p-adic pseudo-reflection) groups\, in which case the
compact Lie groups are replaced by the so-called p-compact groups (a.k.a.
homotopy Lie groups).\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/43
DESCRIPTION:Title: Algebras and superalgebras with (super-)involutions and their poly
nomial identities\nby Onofrio Mario Di Vincenzo (Università di Basili
cata\, Potenza\, Italy) as part of LieJor Online Seminar: Algebras\, repre
sentations\, and applications\n\n\nAbstract\nIn this talk we consider the
*-polynomial identities of algebras with involutions. The positive solutio
n of Specth's problem\, given by Aljadeff\, Giambruno and Karasik in [E. A
ljadeff\, A. Giambruno\, Y. Karasik Polynomial identities with involution\
, super-involutions and the Grassmann envelope\, Proc. Amer. Math. Soc. 14
5 (2017)\, no. 5\,1843-1857]\, for the T*-ideals of the free algebra with
involution\, show the decisive role of the identities of finite dimensiona
l superalgebras with superinvolution. In this talk we consider block-trian
gular matrix algebras related to any sequence of such *-simple superalgebr
as. These *-simple superalgebras are also involved in determining the exac
t value of the correponding exponent as proved in [A. Ioppolo The exponent
for superalgebras with superinvolution\, Linear Algebra and its Applicati
ons Amer. Math. Soc. 555 (2018)\, 1-20]. We review the results in this are
a and we show that that every minimal affine variety of superalgebras with
superinvolution is generated by one of the block triangular matrix algebr
as we introduced\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kanel-Belov (Bar Ilan University\, Israel)
DTSTART:20210805T170000Z
DTEND:20210805T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/44
DESCRIPTION:Title: Evaluations of nonassociative polynomials on finite dimensional al
gebras\nby Alexei Kanel-Belov (Bar Ilan University\, Israel) as part o
f LieJor Online Seminar: Algebras\, representations\, and applications\n\n
\nAbstract\nLet \\(p\\) be a polynomial in several non-commuting variable
s with coefficients in an algebraically closed field \\(K\\) of arbitrary
characteristic. It has been conjectured that for any \\(n\\)\, for \\(p\\)
multilinear\, the image of \\(p\\) evaluated on the set \\(M_n(K)\\) of \
\(n\\) by \\(n\\) matrices is either zero\, or the set of scalar matrices\
, or the set \\(sl_n(K)\\) of matrices of trace 0\, or all of \\(M_n(K)\\)
.
In this talk we will discuss the generalization of this result
for non-associative algebras such as Cayley-Dickson algebra (i.e. algebra
of octonions)\, pure (scalar free) octonion Malcev algebra and basic low
rank Jordan algebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Romanovskiy (Novosibirsk State University\, Russia)
DTSTART:20210812T150000Z
DTEND:20210812T160000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/45
DESCRIPTION:Title: Rigid solvable groups. Algebraic geometry and model theory\nby
Nikolay Romanovskiy (Novosibirsk State University\, Russia) as part of Li
eJor Online Seminar: Algebras\, representations\, and applications\n\n\nAb
stract\nA solvable group \\(G\\) is called rigid\, more precisely \\(m\\)-
rigid\, if there exists a normal series of subgroups \\(G=G_1 > G_2 > \\ld
ots > G_m > G_{m+1}=1\,\\) where all quotients \\(G_i/G_{i+1}\\) are abeli
an and when viewed as right modules over \\(\\mathbb{Z} [G/G_i]\\)\, do no
t have torsion. Free solvable groups and iterated wreath products of torsi
on free abelian groups are rigid\, as well as their subgroups. A rigid gro
up \\(G\\) is termed divisible if elements of the quotient \\(G_i/G_{i+1}\
\) 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 fracti
ons \\(Q(G/G_i)\\) of the ring \\(\\mathbb{Z} [G/G_i]\\) (such a skew-fiel
d exists).
The talk will present the results of the author and A.
Myasnikov. Among them\, on the algebraic geometry of rigid groups\, we st
ate the main two: it is proved that any rigid group is equationally Noethe
rian\, and the coordinate groups of irreducible algebraic sets over a divi
sible rigid group are described. The theory of models of divisible m-rigid
groups is in many ways similar to the classical theory of models of algeb
raically closed fields. The axiomatics of the theory of divisible m-rigid
groups is found\, \\(\\omega\\)-stability is proved\, saturated models are
described\, the elimination of quantifiers is found\, the problems of cal
culating the Morley rank are studied. Model theory results use algebraic g
eometry over divisible rigid groups.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugeny Plotkin (Bar-Ilan University\, Israel)
DTSTART:20210819T170000Z
DTEND:20210819T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/46
DESCRIPTION:Title: Bounded generation and logical properties for linear and Kac-Moody
cases\nby Eugeny Plotkin (Bar-Ilan University\, Israel) as part of Li
eJor Online Seminar: Algebras\, representations\, and applications\n\n\nAb
stract\nWe will survey a series of recent developments in the area of boun
ded generation and first-order descriptions of groups. The goal is to illu
minate the known results relevant to logical characterizations of Chevalle
y and Kac-Moody groups. If time permits I will discuss related questions o
riginated from universal algebraic geometry.\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/47
DESCRIPTION:Title: Dimension formula for Koszul operads\nby Askar Dzhumadil'daev
(Academy of Sciences of Kazakhstan\, Kazakhstan) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nWe g
ive recurrence formula for dimensions of Koszul operads. For example\, dim
ensions of multi-linear parts of Lie-admissible operad satisfy the followi
ng recurrence relations \\(d_n=\\sum_{i=1}^{n-1}\\mu k B_{n-1\,k}(d_1\,\\l
dots\,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}\\equiv -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://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:20260422T213011Z
UID:LieJor_Seminar/48
DESCRIPTION:Title: Classifications of simple Lie (super)algebras and algebras "more i
nteresting" than simple\nby Dimitry Leites (New York University Abu Dh
abi\, United Arab Emirates and Stockholm University\, Sweden) as part of L
ieJor Online Seminar: Algebras\, representations\, and applications\n\n\nA
bstract\nI intend to overview classifications of simple Lie (super)algebra
s of finite dimension and of polynomial growth. Various properties of comp
lex Lie superalgebras resemble same of modular Lie algebras. I will encour
age to consider these classifications without fanaticism: certain non-simp
le Lie (super)algebras\, "close" to simple ones\, are often "better" for u
s than simple ones.\n\nInteresting features of deformations: semi-trivial
deformations and (in super setting) odd parameters.\n\nI'll formulate clas
sification of finite-dimensional simple complex Lie superalgebras\, odd pa
rameters including.\n\nI'll formulate a definition of Lie superalgebra sui
table for any characteristic and classification of simple (finite-dimensio
nal) Lie superalgebras over algebraically closed fields of characteristic
2. With a catch: modulo (a) classification of simple (finite-dimensional)
Lie superalgebras (over the same field) and (b) classification of their gr
adings modulo 2. I'll mention conjectures on classification of modular Lie
algebras and superalgebras.\n\nIs it feasible to classify simple filtered
Lie (super)algebras of polynomial growth? Interesting examples: deforms o
f the Poisson Lie (super)algebras\, Lie (super)algebras of "matrices of co
mplex size"\, etc.\n\nExamples. Double extensions of simple Lie (super)alg
ebras are definitely "more interesting" than the simple objects they exten
d.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ofelia Ronco (Universidad de Talca\, Chile)
DTSTART:20210909T170000Z
DTEND:20210909T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/49
DESCRIPTION:Title: Generalization of dendriform algebras\nby Maria Ofelia Ronco (
Universidad de Talca\, Chile) as part of LieJor Online Seminar: Algebras\,
representations\, and applications\n\n\nAbstract\nIn a joint work with D.
López N. and L.-F. Préville-Ratelle [D. Lopez\, L.-F. Pr&eacu
teville-Ratelle\, M. Ronco\, Algebraic structures defined on \\(m\\)-Dyck
paths\, preprint arxiv:1508.01252 (2015)] we introduce a family of non-sy
mmetric 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 dendriform a
lgebras\, introduced by J.-L. Loday in [J.-L. Loday\, Dialgebras\, in Dial
gebras and related operads\, Lecture Notes in Math.\, 1763\, Springer\, Be
rlin (2001) 7-66]\,
3. the vector space spanned by the set of \\(m
\\)-Dyck paths has a natural structure of free \\({\\mbox{Dyck}^m}\\) alge
bra over one element\,
4. for any \\(k\\geq 1\\)\, there exist de
generacy operators \\(s_i: {\\mbox{Dyck}^m}\\longrightarrow {\\mbox{Dyck}^
{m-1}}\\) and face operators \\(d_j: {\\mbox{Dyck}^m}\\longrightarrow {\\
mbox{Dyck}^{m+1}}\\)\, which defines a simplicial complex in the category
of non-symmetric operads.
The main examples of \\({\\mbox{Dyck}^m}
\\) algebra are the vector spaces spanned by the \\(m\\)-simplices of cert
ain combinatorial Hopf algebras\, like the Malvenuto-Reutenauer algebras a
nd the algebra of packed words.
A well-known result on associativ
e algebras states that\, as \\({\\mathcal S}\\)-module\, the operad of \\(
{\\mbox{Ass}}\\) of associative algebras is the composition \\({\\mbox{As
s}} ={\\mbox{Com}}\\circ {\\mbox{Lie}}\\)\, where \\({\\mbox{Com}}\\) is t
he operad of commutative algebras and \\({\\mbox{Lie}}\\) is the operad of
Lie algebras. The version of this result for dendriform algebras (see [M.
Ronco\, Eulerian idempotents and Milnor-Moore theorem for certain non-coc
ommutative Hopf algebras\, J. of Algebra 254 (2002) 152-172.])\, is that \
\({\\mbox{Dend}} = {\\mbox{Ass}}\\circ {\\mbox{Brace}}\\)\, where \\({\\mb
ox{Brace}}\\) is the operad of brace algebras\, defined in [M. Gerstenhabe
r\, A. Voronov\, Homotopy G-algebras and moduli space operad\, Internat.
Math. Research Notices (1995)\, 141-153.] and [E. Getzler\, Cartan homotop
y formulas and the Gauss-Manin connection in cyclic homology\, Israel Math
. Conf. Proc. 7 (1993)\, 65-78.].
Our goal is to introduce the no
tion of \\(m\\)-brace algebra\, for \\(m\\geq 2\\)\, and prove that there
exists a Poincaré-Birkoff-Witt Theorem in this context\, stating tha
t \\({\\mbox{Dyck}^m} = {\\mbox{Ass}}\\circ {\\mbox{m-Brace}}\\).
Joint work with: Muriel Livernet\,Dept. of Mathématiques\, Univ. de
Paris-Diderot\, France.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Vojtechovsky (Denver University\, USA)
DTSTART:20210916T170000Z
DTEND:20210916T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/50
DESCRIPTION:Title: Quandles and other classes of set-theoretic solutions of the Yang-
Baxter equation\nby Petr Vojtechovsky (Denver University\, USA) as par
t of LieJor Online Seminar: Algebras\, representations\, and applications\
n\n\nAbstract\nQuandles are algebraic structures designed to mesh with the
Reidemeister moves of knot theory. Joyce and Matveev showed that quandles
give rise to a complete invariant of oriented knots. Since the Yang-Baxte
r equation resembles the third Reidemeister move\, it is not surprising th
at quandles also form a class of set-theoretic solutions of the Yang-Baxte
r equation. In this talk I will explain how quandles and connected quandle
s can be enumerated up to isomorphism and list a few open problems. I will
also present two additional classes (involutive and idempotent) of set-th
eoretic solutions of the Yang-Baxter equation with rich algebraic theory.\
n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valery Bardakov (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20210923T170000Z
DTEND:20210923T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/51
DESCRIPTION:Title: Quandles and quandle rings\nby Valery Bardakov (Sobolev Instit
ute of Mathematics\, Novosibirsk\, Russia) as part of LieJor Online Semina
r: Algebras\, representations\, and applications\n\n\nAbstract\nAt the fir
st part of my talk I give a definition and examples of racks and quandles\
, explain their connection with knot theory and with set-theoretic solutio
ns of the Yang-Baxter equation. Further I introduce some properties of qua
ndles: residually finiteness\, orderability\, and formulate results on qua
ndles which have these properties.\n\nThe second part of my talk is dedica
ted to quandle rings. I introduce generalized quandle ring\, augmented ide
al\, describe relationships between subquandles of the given quandle and i
deals of the associated quandle ring. The construction of the quotient qua
ndle leads to a correspondence between subquandles of the given quandle an
d ideals of the quandle ring.\n\nI formulate some results on zero-divisors
in quandle rings. Some of these results answer a question of M. Elhamdadi
\, N. Fernando and B. Tsvelikhovskiy [J. Algebra\, 526 (2019)\, 166-187] o
n quandle rings which do not have zero-divisors.\n\nWe discuss a problem o
f the computation of idempotents in quandle rings. The computation of idem
potents is then used to determine automorphism groups of some quandle ring
s.\n\nI introduce the commutator width of quandle rings and compute the pr
ecise commutator width for some quandle rings.\n\nWe also discuss relation
s of quandle algebras with other well-known non-associative algebras 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://researchseminars.org/talk/LieJor_Seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Semrl (University of Ljubljana\, Slovenia)
DTSTART:20210930T170000Z
DTEND:20210930T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/52
DESCRIPTION:Title: On Wigner's theorem\nby Peter Semrl (University of Ljubljana\,
Slovenia) as part of LieJor Online Seminar: Algebras\, representations\,
and applications\n\n\nAbstract\nSome recent improvements of Wigner's unita
ry-antiunitary theorem will be presented. A connection with Gleason's theo
rem will be explained.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael J. Larsen (Indiana University\, USA)
DTSTART:20211007T170000Z
DTEND:20211007T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/53
DESCRIPTION:Title: Quotients of normal subsets in simple groups\nby Michael J. La
rsen (Indiana University\, USA) as part of LieJor Online Seminar: Algebras
\, representations\, and applications\n\n\nAbstract\nLet \\(G\\) be a fini
te simple group and \\(S\\) a normal subset of \\(G\\). If \\(|G|\\) is l
arge enough in terms of \\(|S|/|G|\\)\, can we deduce that every element o
f \\(G\\) can be expressed as \\(x y^{-1}\\) for \\(x\\) and \\(y\\) eleme
nts of \\(S\\)? Shalev\, Tiep\, and I have proven that this is true assum
ing \\(G\\) is an alternating group or a group of Lie type in bounded rank
\, but the question remains open for classical groups of high rank over sm
all fields. I will say something about the methods of proof\, which invol
ve both character methods and geometric ideas and also say something about
the more general question of covering \\(G\\) by \\(ST\\) where \\(S\\) a
nd \\(T\\) are large normal subsets.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Rowen (Bar-Ilan University\, Israel)
DTSTART:20211014T170000Z
DTEND:20211014T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/54
DESCRIPTION:Title: Finitely generated axial algebras\nby Louis Rowen (Bar-Ilan Un
iversity\, Israel) as part of LieJor Online Seminar: Algebras\, representa
tions\, and applications\n\n\nAbstract\nThis lecture is a continuation of
the general talk given at the Drensky conference last month\, on axial alg
ebras\, which are (not necessarily commutative\, not necessarily associati
ve) algebras generated by semisimple idempotents. After a review of the de
finitions\, we investigate the key question\, being\, "Under what conditio
ns must an axial algebra be finite dimensional?" Krupnik showed that 3 ide
mpotents can generate arbitrarily large dimensional associative algebras (
and thus infinite dimensional algebras via an ultraproduct argument)\, so
some restriction is needed. We consider "primitive" axes\, in which the le
ft and right eigenspaces having eigenvalue 1 are one-dimensional.
Hall\, Rehren\, Shpectorov solves obtained a positive answer for commutat
ive axial algebras of "Jordan type" \\(\\lambda \\neq \\frac{1}{2}\\)\, al
though the proof relies on the classification of simple groups and the giv
en bound of the dimension is rather high. Gorshkov and Staroletov provided
a sharp bound for 3-generated commutative axial algebras of "Jordan type"
. Our objective in this project is give a noncommutative version and indic
ate how to investigate 4-generated commutative axial algebras of "Jordan t
ype"\, in terms of the regular representation.
Our method is to b
uild an associative algebra from the adjoint algebra of \\(A\\)\, which ha
s a strictly larger dimension which nevertheless also is finite dimensiona
l.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oksana Bezuschak (Kyiv Taras Shevchenko University\, Ukraine)
DTSTART:20211021T170000Z
DTEND:20211021T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/55
DESCRIPTION:Title: Locally matrix algebras and algebras of Mackey\nby Oksana Bezu
schak (Kyiv Taras Shevchenko University\, Ukraine) as part of LieJor Onlin
e Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nIn
this talk we will discuss:\n\n1. Tensor decompositions of locally matrix
algebras and their parametrization by Steinitz numbers.\n\n2. Automorphism
s and derivations of locally matrix algebras.\n\n3. Automorphisms and deri
vations of Mackey algebras and Mackey groups. In particular\, we describe
automorphisms of all infinite simple finitary torsion groups (in the class
ification of J.Hall) and derivations of all infinite-dimensional simple fi
nitary Lie algebras (in the classification of A.Baranov and H.Strade).\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aron Simis (Universidade Federal de Pernambuco\, Brazil)
DTSTART:20211028T170000Z
DTEND:20211028T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/56
DESCRIPTION:Title: Some conjectures in commutative algebra\nby Aron Simis (Univer
sidade Federal de Pernambuco\, Brazil) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\nThere are "big
" conjectures and not-so-big ones in the field. Some of the first have eit
her been solved (often by unexpected tools) or are still pending like a fr
uit on the top of a tree with delicate branches\, making it often hard for
a layperson like some of us. This talk is about more modest conjectures\,
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://researchseminars.org/talk/LieJor_Seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vsevolod Gubrev (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20211104T170000Z
DTEND:20211104T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/57
DESCRIPTION:Title: Embedding of Loday algebras into Rota-Baxter algebras\nby Vsev
olod Gubrev (Sobolev Institute of Mathematics\, Novosibirsk\, Russia) as p
art of LieJor Online Seminar: Algebras\, representations\, and application
s\n\n\nAbstract\nIt is known that every Rota-Baxter algebra of weight 0 (1
) gives rise to a prealgebra (postalgebra). In 2013\, it was proved that e
very 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 given pre-
or post-Lie algebra.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Grishkov (Universidade de São Paulo\, Brazil)
DTSTART:20211111T170000Z
DTEND:20211111T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/58
DESCRIPTION:Title: 12th Hilbert problem and Carlitz-Drinfeld-Anderson modules\nby
Alexandre Grishkov (Universidade de São Paulo\, Brazil) as part of LieJo
r Online Seminar: Algebras\, representations\, and applications\n\n\nAbstr
act\nThe well known Kronecker-Weber theorem affirms that every finite abel
ian extension of the field \\(Q\\) of rational numbers belongs to some cy
clotomic extension \\(Q(t|t^n=1)\\). In his 12th problem D.Hilbert asked h
ow to generalize this theorem for other global fields. In this talk\, we g
ive the exposition of atual state of this problem together with the conne
ction with Carlitz-Drinfeld-Anderson modules.
Recall that Anders
on 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://researchseminars.org/talk/LieJor_Seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo Aguiar (Cornell University\, USA)
DTSTART:20211202T150000Z
DTEND:20211202T160000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/59
DESCRIPTION:Title: Lie theory relative to a hyperplane arrangement\nby Marcelo Ag
uiar (Cornell University\, USA) as part of LieJor Online Seminar: Algebras
\, representations\, and applications\n\n\nAbstract\nA result due to Joyal
\, Klyachko\, and Stanley relates free Lie algebras to partition lattices.
We will discuss the precise relationship and interpret the result in term
s of the braid hyperplane arrangement. We will then extend this result to
arbitrary (finite\, real\, and central) hyperplane arrangements\, and do t
he same with several additional aspects of classical Hopf-Lie theory. The
Tits monoid of an arrangement\, and the notion of lune\, play central role
s in the discussion. This is joint work with Swapneel Mahajan.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sokolov (UFABC\, Brazil)
DTSTART:20211209T170000Z
DTEND:20211209T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/60
DESCRIPTION:Title: Non-Abelian Poisson brackets on projective spaces\nby Vladimir
Sokolov (UFABC\, Brazil) as part of LieJor Online Seminar: Algebras\, rep
resentations\, and applications\n\n\nAbstract\nWe discuss nonabelian Poiss
on structures on affine and projective spaces over \\(\\mathbb{C}\\). We a
lso construct a class of examples of nonabelian Poisson structures on \\(\
\mathbb{C} P^{n-1}\\) for \\(n>2\\). These nonabelian Poisson structures d
epend on a modular parameter \\(\\tau\\in\\mathbb{C}\\) and an additional
discrete parameter \\(k\\in\\mathbb{Z}\\)\, where \\(1\\leq k< n\\) and
\\(k\,n\\) are coprime. The abelianization of these Poisson structures ca
n be lifted to the quadratic elliptic Poisson algebras \\(q_{n\,k}(\\tau)\
\).\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arturo Pianzola (University of Alberta\, Canada)
DTSTART:20211125T170000Z
DTEND:20211125T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/61
DESCRIPTION:Title: Derivations of twisted forms of Lie algebras\nby Arturo Pianzo
la (University of Alberta\, Canada) as part of LieJor Online Seminar: Alge
bras\, representations\, and applications\n\n\nAbstract\nThe main purpose
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 au
dience is familiar with torsors. Definitions and examples will be given. T
he main application in this case is to provide a general framework (relati
ve sheaves of Lie algebras) that explains/justifies a known result about t
he derivations of multiloop algebras.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iryna Kashuba (Universidade de São Paulo\, Brazil)
DTSTART:20211202T170000Z
DTEND:20211202T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/62
DESCRIPTION:Title: On the Free Jordan algebras\nby Iryna Kashuba (Universidade de
São Paulo\, Brazil) as part of LieJor Online Seminar: Algebras\, represe
ntations\, and applications\n\n\nAbstract\nWe will discuss a conjecture fo
r the character of the homogenous components of the free Jordan algebra o
n \\(d\\) generators as a \\(GL(d)\\)-module. This is joint work with Oliv
ier Mathieu.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Koshlukov (UNICAMP\, Brazil)
DTSTART:20220217T170000Z
DTEND:20220217T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/64
DESCRIPTION:Title: Gradings on upper triangular matrices\nby Plamen Koshlukov (UN
ICAMP\, Brazil) as part of LieJor Online Seminar: Algebras\, representatio
ns\, and applications\n\n\nAbstract\nGradings on upper triangular matrices
.\; Plamen Koshlukov (UNICAMP\, Brazil)\; The upper triangular matrix alge
bras are important in Linear Algebra\, and represent a powerful tool in Ri
ng Theory. They also appear in the theory of PI algebras.
In addi
tion to the usual associative product\, one can consider the Lie bracket a
nd also the symmetric (Jordan) product on the upper triangular matrices. <
br>
We discuss the group gradings on the upper triangular matrices vie
wed as an associative\, Lie and Jordan algebra\, respectively. Valenti and
Zaicev proved that the associative gradings are\, in a sense\, given by g
radings on the matrix units. Di Vincenzo\, Valenti and Koshlukov classifie
d 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 Yukihide a
nd Koshlukov.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Holger Petersson (FernUniversität in Hagen\, Germany)
DTSTART:20220224T170000Z
DTEND:20220224T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/65
DESCRIPTION:Title: Octonions and Albert algebras over commutative rings\nby Holge
r Petersson (FernUniversität in Hagen\, Germany) as part of LieJor Online
Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nIn
the first part of the lecture\, I will focus on two properties of octonion
algebras that are known to hold over fields but fail over arbitrary commu
tative rings: their enumeration by means of the Cayley-Dickson constructio
n\, and the norm equivalence theorem. In the second part\, I will describe
a new approach to the first Tits construction of Albert algebras that\, e
ven over fields\, is more general than the classical one and sheds some ne
w light on the classification problem for reduced Albert algebras over com
mutative rings.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Racine (Ottawa University\, Canada)
DTSTART:20220303T170000Z
DTEND:20220303T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/66
DESCRIPTION:Title: Lie Algebras afforded by Jordan algebras with particular Attention
to Albert Algebras\nby Michel Racine (Ottawa University\, Canada) as
part of LieJor Online Seminar: Algebras\, representations\, and applicatio
ns\n\n\nAbstract\nGiven a (quadratic) Jordan algebra J over a ring k\, one
obtains three Lie algebras\, the derivation algebra\, the structure algeb
ra\, and the Tits algebra. We are particularly interested in the case wher
e J is an Albert algebra.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Guerassimov (UFMG\, Brazil)
DTSTART:20220310T170000Z
DTEND:20220310T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/67
DESCRIPTION:Title: Random walks on groups. An introduction\nby Victor Guerassimov
(UFMG\, Brazil) as part of LieJor Online Seminar: Algebras\, representati
ons\, and applications\n\n\nAbstract\nGeometric methods proved to be usefu
l in the study of some groups. However the geometry of the Cayley graph of
a group is rather different from the geometry of classical geometric obje
cts such as homogeneous spaces of Lie groups. The similarity between these
two geometries grows as the scale of observation increases. And the asymp
tototic behavior of them shows surprising similarity. Random walks is an e
ssential tool in studying large-scale geometry of groups. On the other han
d it is an interesting object for probabilists since many properties of ge
neral stochastic processes are manifested here in a rather simple form. In
my talk\, I will provide an elementary introduction to this vast area. No
special knowledge beyond the usual university mathematics is required.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Stolin (Chalmers University of Technology\, Sweden)
DTSTART:20220317T170000Z
DTEND:20220317T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/68
DESCRIPTION:Title: 40 years of Lie bialgebras: From definition to classification\
nby Alexander Stolin (Chalmers University of Technology\, Sweden) as part
of LieJor Online Seminar: Algebras\, representations\, and applications\n\
n\nAbstract\nThe history of Lie bialgebras began with the paper where the
Lie bialgebras were defined: V. G. Drinfeld\, "Hamiltonian structures on L
ie groups\, Lie bialgebras and the geometric meaning of the classical 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 celebrate
40 years of Lie bialgebras in mathematics and to explain how these import
ant algebraic structures can be classified. This classification goes "hand
in hand" with the classification of the so-called Manin triples and Drinf
eld doubles also introduced in Drinfeld's paper cited above.
The
ingenious idea how to classify Drinfeld doubles associated with Lie algebr
as possessing a root system is due to F. Montaner and E. Zelmanov. In part
icular\, using their approach the speaker classified Lie bialgeras\, Manin
triples and Drinfeld doubles associated with a simple finite dimensional
Lie algebra g (the paper was based on a private communication by E. Zelman
ov and it was published in Comm. Alg. in 1999).
Further\, in 201
0\, 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. Maximov\
, E. Zelmanov and the speaker published an Arxive preprint\, where they ma
de a crucial progress towards a complete classification of Manin triples
and Lie bialgebra structures on g[[u]].
Of course\, it is impossi
ble to compress a 40 years history of the subject in one talk but the spe
aker will try his best to do this.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuriy A. Drozd (Kiev University\, Ukraine)
DTSTART:20220324T170000Z
DTEND:20220324T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/69
DESCRIPTION:Title: Morita Theory for noncommutative varieties\nby Yuriy A. Drozd
(Kiev University\, Ukraine) as part of LieJor Online Seminar: Algebras\, r
epresentations\, and applications\n\n\nAbstract\nMorita theorem gives a cr
iterion of equivalence of categories of modules over rings. On the other h
and\, Gabriel proved that the category of coherent sheaves defines a Noeth
erian 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-commutative s
cheme completely defines its center and the schemes with the same center a
re Morita equivalent if and only if one of them is isomorphic to the schem
e of endomorphisms of a local progeneretor of the other.
It is a comm
on work with Igor Burban.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio M. Peralta (Universidad de Granada\, Spain)
DTSTART:20220331T170000Z
DTEND:20220331T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/70
DESCRIPTION:Title: How can we apply Jordan structures to reinterpret Wigner-Uhlhorn t
heorem?\nby Antonio M. Peralta (Universidad de Granada\, Spain) as par
t of LieJor Online Seminar: Algebras\, representations\, and applications\
n\n\nAbstract\nUp to date\, much has been written about E. Wigner and U. U
hlhron theorems and their importance for physics and mathematics. For the
sake of conciseness\, let us go straight to some of the starring results.
There are six mathematical models employed in quantum mechanics\, among th
em we have:- The C\\(^*\\)-algebra \\(B(H)\\) of bounded operators&#
59
- 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 projection
s in \\(B(H)\\)\,
where \\(H\\) is a complex Hilbert space.
Th
e natural automorphisms of these mathematical models (i.e.\, the bijection
s \\(f\\) on these sets preserving the corresponding relevant structure: a
ssociative product and involution\, Jordan product\, and orthogonality and
order between subspaces or projections) represent the symmetry groups of
quantum mechanics and are endowed with natural topologies induced by the p
robabilistic structure of quantum mechanics. It is known that these symmet
ry groups are all isomorphic when dim\\((H)\\geq 3\\). The last restrictio
n exclude rank two\, where there are no more than two orthogonal projectio
ns. This equivalence can be seen as the celebrated Wigner unitary-antiunit
ary theorem.
By replacing the set of projections \\(\\mathcal{P}(H)
\\) by the wider set\, \\(PI(H) = \\mathcal{U}(B(H))\\)\, of all partial
isometries on \\(H\\)\, L. Molná proved in [3] the following result: L
et \\(H\\) be a complex Hilbert space with dim\\((H)\\geq 3\\). Suppose th
at \\(\\Phi : \\mathcal{U}(B(H))\\to \\mathcal{U}(B(H))\\) is a bijective
transformation which preserves the natural partial ordering and the orthog
onality between partial isometries in both directions. If \\(\\Phi\\) is c
ontinuous (in the operator norm) at a single element of \\(\\mathcal{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 partial is
ometry orthogonal to \\(e\\).
During this talk we shall present new
results\, obtained in collaboration with Y. Friedman (see [1])\, showing
that an extension of the previous results is possible in the case of a bij
ection between the lattices of tripotents of two Cartan factors and atomic
JBW\\(^*\\)-triples non-containing rank-one Cartan factors. These new res
ult provide new models to understand the quantum models. We shall also see
how the results provide new alternatives to complement recent studies by
J. Hamhalter [2] proving that the set of partial isometries with its par
tial order and orthogonality relation is a complete Jordan invari
ant for von Neumann algebras.
References
[1] Y. Friedm
an\, A.M. Peralta\, Representation of symmetry transformations on the sets
of tripotents of spin and Cartan factors\, to appear in Analysis and M
athematical Physics\, https://doi.org/10.1007/s13324-021-00644-8\, ar
Xiv: 2101.00670.
[2] J. Hamhalter\, Dye's theorem for tripotents in von
Neumann algebras and JBW\\(^*\\)-triples\, Banach J. Math. Anal. <
b>15 (2021)\, no. 3\, Paper No. 49\, 19 pp.
[3] L. Molnár\, On
certain automorphisms of sets of partial isometries\, Arch. Math. (Base
l) 78\, no. 1\, 43--50 (2002).
[4] U. Uhlhorn\, Representati
on of symmetry transformations in quantum mechanics\, Ark. Fysik 23\, 307--340 (1963).
[5] E.P. Wigner\, Gruppentheorie und ihre
Anwendung auf die Quantenmechanik der Atomspektrum\, Fredrik Vieweg u
nd Sohn\, 1931.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Shumyatsky (UnB\, Brazil)
DTSTART:20220407T170000Z
DTEND:20220407T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/71
DESCRIPTION:Title: Commuting probability for subgroups of a finite group\nby Pave
l Shumyatsky (UnB\, Brazil) as part of LieJor Online Seminar: Algebras\, r
epresentations\, and applications\n\n\nAbstract\nThis is a joint work with
Eloisa Detomi (University of Padova).
If \\(K\\) is a subgroup o
f a finite group \\(G\\)\, the probability that an element of \\(G\\) comm
utes with an element of \\(K\\) is denoted by \\(Pr(K\,G)\\). The probabil
ity that two randomly chosen elements of \\(G\\) commute is denoted by \\(
Pr(G)\\). A well known theorem\, due to P. M. Neumann\, says that if \\(G\
\) is a finite group such that \\(Pr(G)\\geq\\epsilon\\)\, then \\(G\\) ha
s a nilpotent normal subgroup \\(T\\) of class at most \\(2\\) such that b
oth the index \\([G:T]\\) and the order \\(|[T\,T]|\\) are \\(\\epsilon\\)
-bounded.
In the talk we will discuss a stronger version of Neum
ann'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\\) and a sub
group \\(B\\leq K\\) such that the indexes \\([G:T]\\) and \\([K:B]\\) and
the order of the commutator subgroup \\([T\,B]\\) are \\(\\epsilon\\)-bou
nded.
We will also discuss a number of corollaries of this resul
t. A typical application is that if in the above theorem \\(K\\) is the ge
neralized Fitting subgroup \\(F^*(G)\\)\, then \\(G\\) has a class-2-nilpo
tent normal subgroup \\(R\\) such that both the index \\([G:R]\\) and the
order of the commutator subgroup \\([R\,R]\\) are \\(\\epsilon\\)-bounded.
\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo do Nascimento Marcos (IME-USP\, Brazil)
DTSTART:20220414T170000Z
DTEND:20220414T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/72
DESCRIPTION:Title: Koszul e homogeneous triples for algebras with two relations\n
by Eduardo do Nascimento Marcos (IME-USP\, Brazil) as part of LieJor Onlin
e Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nTh
is talk is based on a joint work with Yury Volkov. We define the category
of homogeneous triples\, which is equivalent to the category of graded alg
ebras\, with a fixed semisimple degree zero part. We apply the results to
algebras whose defining ideal has two generators\, and give a partial clas
sification.
We thank Fapesp\, grant 2018/23690-6\, for the suppo
rt.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Miasnikov (Stevens Institute of Technology\, USA)
DTSTART:20220421T170000Z
DTEND:20220421T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/73
DESCRIPTION:Title: Rich groups and weak second order logic\nby Alexei Miasnikov (
Stevens Institute of Technology\, USA) as part of LieJor Online Seminar: A
lgebras\, representations\, and applications\n\n\nAbstract\n"What can one
describe by first-order formulas in a given group A?" - is an old and inte
resting question. Of course\, this depends on the group A. For example\, i
n a free group only cyclic subgroups (and the group itself) are definable
in the first-order logic\, but in a free monoid of finite rank any finitel
y 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. Surprisingl
y\, there are a lot of interesting groups\, rings\, semigroups\, etc.\, wh
ich are rich. I will describe various algebraic\, geometric\, and algorith
mic properties that are first-order definable in rich groups and apply the
se to some open problems. Weak second order logic can be introduced into a
lgebraic structures in different ways: via HF-logic\, or list superstructu
res over A\, or computably enumerable infinite disjunctions and conjunctio
ns\, or via finite binary predicates\, etc. I will describe a particular f
orm of this logic which is especially convenient to use in algebra and sho
w how to effectively translate such weak second order formulas into the eq
uivalent first-order ones in the case of a rich group A.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Sapir (Vanderbilt University\, USA)
DTSTART:20220428T170000Z
DTEND:20220428T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/74
DESCRIPTION:Title: Subgroups of the R.Thompson group F\nby Mark Sapir (Vanderbilt
University\, USA) as part of LieJor Online Seminar: Algebras\, representa
tions\, and applications\n\n\nAbstract\nThis is joint work with Gili Golan
-Polak. We describe the so-called closed subgroups of F. In particular\, w
e construct a subgroup of F with easily decidable membership problem and u
ndecidable conjugacy problem\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Penkov (Jacobs University Bremen\, Germany)
DTSTART:20220505T170000Z
DTEND:20220505T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/75
DESCRIPTION:Title: New analogues of category O for the Lie algebra \\(sl(\\infty)\\)<
/a>\nby Ivan Penkov (Jacobs University Bremen\, Germany) as part of LieJor
Online Seminar: Algebras\, representations\, and applications\n\n\nAbstra
ct\nI will recall several highest weight categories for \\(sl(\\infty)\\)
studied in the past decade\, and will then report on the newest highest we
ight categories introduced by P. Zadunaisky. A main point is the use a non
-obvious Borel subalgebra plus a semi-large annihilator condition. As a si
de effect\, the new categories produce interesting and challenging combina
torics.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bahturin (Memorial University of Newfoundland\, Canada)
DTSTART:20220512T170000Z
DTEND:20220512T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/76
DESCRIPTION:Title: Group Gradings and Actions of Pointed Hopf Algebras\nby Yuri B
ahturin (Memorial University of Newfoundland\, Canada) as part of LieJor O
nline Seminar: Algebras\, representations\, and applications\n\n\nAbstract
\nPointed Hopf algebras are a wide class of Hopf algebras\, including grou
p algebras and enveloping algebras of Lie algebras. In this talk\, based o
n a recent work with Susan Montgomery\, we study actions of pointed Hopf a
lgebras on simple algebras. These actions are known to be inner\, as in th
e case of Skolem - Noether theorem. We try to give explicit descriptions\,
whenever possible\, and consider Taft algebras\, their Drinfeld doubles a
nd some quantum groups.\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/77
DESCRIPTION:Title: Algebraic sets\, ideals of points and the Hilbert's Nullstellensat
z theorem for skew PBW extensions\nby José Oswaldo Lezama Serrano (Un
iversidad Nacional de Colombia\, Colombia) as part of LieJor Online Semina
r: Algebras\, representations\, and applications\n\n\nAbstract\nIn this ta
lk we define the algebraic sets and the ideal of points for bijective skew
PBW extensions with coefficients in left Noetherian domains. Some propert
ies of affine algebraic sets of commutative algebraic geometry will be ext
ended\, in particular\, a Zariski topology will be constructed. Assuming a
dditionally that the extension is quasi-commutative with polynomial center
and the ring of coefficients is an algebraically closed field\, we will p
rove an adapted version of Hilbert's Nullstellensatz theorem that covers t
he classical one. The Gröbner bases of skew PBW extensions will be used f
or defining the algebraic sets and for proving the main theorem. Many key
algebras and rings coming from mathematical physics and non-commutative al
gebraic geometry are skew PBW extensions.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Efim Zelmanov (University of California\, San Diego\, USA)
DTSTART:20220526T170000Z
DTEND:20220526T180000Z
DTSTAMP:20260422T213011Z
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://researchseminars.org/talk/LieJor_Seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David A. Jordan (Sheffield University\, UK)
DTSTART:20220602T170000Z
DTEND:20220602T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/79
DESCRIPTION:Title: Skew derivations of quantum spaces\nby David A. Jordan (Sheffi
eld University\, UK) as part of LieJor Online Seminar: Algebras\, represen
tations\, and applications\n\n\nAbstract\nLet $n$ be a positive integer an
d let $Q = (q_{ij})$ be a multipicatively antisymmetric $n \\times n$ ma
trix\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 $n$-sp
ace $R:=\\mathcal{O}_Q(\\mathbb{K}^n)$ is the $\\mathbb{K}$-algebra ge
nerated 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 derivati
ons $\\mathrm{Der}(R)$ is well-understood through work of Alev and Chamari
e in 1982\, less is known about the \nspace $\\mathrm{Der}_\\sigma(R)$ of
$\\sigma$-derivations of $R$. The only case in the literature where 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 paper by A
lmulhem and Brzezi\\'{n}ski that was motivated by differential geometry. T
his talk will discuss the classification of the \n$\\sigma$-derivations 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 iterated Or
e extensions of $\\mathbb{K}$. Any such classification must include the <
i>inner $\\sigma$-derivations of $R$\, that is those for which there e
xists $a\\in R$ 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 noncommutativ
e algebra namely localization and grading\, in this case by $\\mathbb{Z}^n
$. Localization at the set $\\{x_1^{d_1}x_2^{d_2}\\dots x_n^{d_n}\\}$ yiel
ds the quantum $n$-torus $T:=\\mathcal{O}_Q((\\mathbb{K}^*)^n)$ to
which $\\sigma$ and all $\\sigma$-derivations extend. A $\\sigma$-derivati
on $\\delta$ 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 $\\sigma$-derivatio
n of $T$ is a unique linear combination of homogeneous $\\sigma$-derivatio
ns. It turns out that if $\\delta$ is a homogeneous $\\sigma$-derivation o
f $T$ then either the automorphism $\\sigma$ is inner or the $\\sigma$-der
ivation $\\delta$ is inner and the Ore extension $T[x\;\\sigma\,\\delta]$
can\, by a change of variables\, be expressed as an Ore extension of eithe
r automorphism type or derivation type. This dichotomy influences the spac
e\n$\\mathrm{Der}_\\sigma(R)$ which can be identified with $\\{\\delta\\in
\\mathrm{Der}_\\sigma(T) :\\delta(R)\\subseteq R\\}$. The most obvious $\
\sigma$-derivations included here are\nthe homogeneous $\\sigma$-derivatio
ns of weight $(d_1\,d_2\,\\dots\, d_n)$ where each $d_i\\geq 0$\, but more
interesting are those for which one $d_i=-1$. There are two types of thes
e\, depending on whether $\\sigma$ or $\\delta$ is inner on $T$. In the la
tter case we are in a common situation where a $\\sigma$-derivation of a r
ing $R$ is not inner on $R$ but becomes inner on the localization of $R$ a
t the powers of a normal element of $R$\, giving rise to a distinguished n
ormal or central element of the Ore extension $R[x\;\\sigma\,\\delta]$.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (Université de Strasbourg\, France)
DTSTART:20220609T170000Z
DTEND:20220609T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/80
DESCRIPTION:Title: New examples of Nielsen-Schreier varieties of algebras\nby Vla
dimir Dotsenko (Université de Strasbourg\, France) as part of LieJor Onli
ne Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nA
variety of algebras is said to be a Nielsen-Schreier variety if every sub
algebra 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 criterio
n\, we show\, in particular\, that the variety of all pre-Lie algebras (al
so known as right-symmetric algebras) is Nielsen-Schreier\, and that\, qui
te surprisingly\, there are already infinitely many Nielsen-Schreier varie
ties of algebras with one binary operation and identities of degree three.
This is joint work with with Ualbai Umirbaev.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT\, USA)
DTSTART:20220616T170000Z
DTEND:20220616T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/81
DESCRIPTION:Title: Weak Jordan algebras in characteristic 5 and tensor categories
\nby Pavel Etingof (MIT\, USA) as part of LieJor Online Seminar: Algebras\
, representations\, and applications\n\n\nAbstract\nWe propose a new algeb
raic structure\, called a weak Jordan algebra\, which we define outside of
characteristics 2\,3. Any Jordan algebra is a weak Jordan algebra\, and t
he converse holds in characteristics different from 5. However\, in charac
teristic 5 there are many examples of simple weak Jordan algebras which ar
e not Jordan\, and not even power associative - they are only power associ
ative up to degree 5 (note that by a theorem of Albert\, an algebra in cha
racteristic 0 or >=7 which is power associative up to degree 5 and even 4
is power associative in all degrees). These algebras correspond (via a ver
sion of the Kantor-Koehler-Tits construction) to Lie algebras in the Fibon
acci tensor category Fib in characteristic 5\, which can be obtained 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 the notio
n of a weak Jordan algebra as an example from a new subject that may be ca
lled "Lie theory in tensor categories".
This is joint work with A.
Kannan and V. Ostrik.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Dokuchaev (IME-USP (Brazil))
DTSTART:20220623T170000Z
DTEND:20220623T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/82
DESCRIPTION:Title: Strong equivalence of graded algebras\nby Misha Dokuchaev (IME
-USP (Brazil)) as part of LieJor Online Seminar: Algebras\, representation
s\, and applications\n\n\nAbstract\nWe introduce the notion of a strong eq
uivalence between graded algebras and prove that any partially-strongly-gr
aded 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-graded-equ
ivalence preserves strong gradings and is nicely related to Morita equival
ence of product partial actions. Furthermore\, we show that strongly-grade
d-equivalent partially-strongly-graded algebras with orthogonal local unit
s are stably isomorphic as graded algebras. This is a part of a joint prep
rint with Fernando Abadie and Ruy Exel.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Lopez-Permouth (Ohio University\, USA)
DTSTART:20220630T170000Z
DTEND:20220630T180000Z
DTSTAMP:20260422T213011Z
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: Algebra
s\, representations\, and applications\n\n\nAbstract\nWhile mutual congeni
ality of bases has been known to guarantee that basic modules from so rela
ted bases are isomorphic\, the question of what can be said about isomorph
ism of basic modules in general has remained open. We show that neither of
two possible extremes must hold. For some algebras\, it is possible\, for
basic modules to be non-isomorphic. Also\, it is possible\, for some alg
ebras\, that all basic modules be isomorphic.
We show that there a
re at least as many pairwise non-isomorphic basic modules over the \\(F\\)
-algebra \\(F[x]\\) of polynomials in a single variable as there are eleme
nts in \\(F\\). We show that basic modules over \\(F[x]\\) can be non-iso
morphic when they are induced by discordant bases and also even when there
is a (non-mutual) congeniality among them. In the process and as a byprod
uct\, we introduce the notion of domains of divisibility of modules over a
rbitrary rings and explore some of the properties of a divisibility profil
e.
At the opposite end of the spectrum\, we present an algebra whe
re all basic modules are isomorphic\, regardless of congeniality.
This is a report on joint work with: C. Arellano\, P. Aydogdu\, R. Muhamma
d\, and M. Zailaee.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Ezequiel Angiono (National University of Cordoba\, Argentina)
DTSTART:20220707T170000Z
DTEND:20220707T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/84
DESCRIPTION:Title: Finite-dimensional pointed Hopf algebras over central extensions o
f abelian groups\nby Ivan Ezequiel Angiono (National University of Cor
doba\, Argentina) as part of LieJor Online Seminar: Algebras\, representat
ions\, and applications\n\n\nAbstract\nOne of the most studied kinds of fi
nite-dimensional Hopf algebras is the family of pointed ones: it means tha
t the coradical is the algebra of the group-like elements. When the group
is abelian\, all such examples are known following the so-called Lifting M
ethod by Andruskiewitsch-Schneider and include deformations of small quant
um groups\, their super analogues and some exceptional examples of Nichols
algebras. When the group is not abelian\, the classification is not known
yet. Even more\, the first step of the Lifting Method (the computation of
all finite-dimensional Nichols algebras) has not been completed: the clas
sification has been performed by Heckenberger-Vendramin when the elements
in degree one form a non-simple Yetter-Drinfeld module\, and consist of lo
w rank exceptions and large rank families.\n\nIn this talk we will present
finite-dimensional Hopf algebras whose coradical is the group algebra of
a central extension of an abelian group. They fall into families associate
d with a simple Lie algebra together with a Dynkin diagram automorphism.\n
\nWe will show conversely that every finite-dimensional pointed Hopf algeb
ra over a non-abelian group with a non-simple infinitesimal braiding is of
this form for large rank families. The proof follows the steps of the Lif
ting Method. Indeed we prove that the large rank families are cocycle twis
ts of Nichols algebras constructed by Lentner as foldings of Nichols algeb
ras of Cartan type over abelian groups by outer automorphisms. This enable
s us to give uniform Lie-theoretic descriptions of the large rank families
\, prove generation in degree one and construct liftings.\n\nWe also show
that every lifting is a cocycle deformation of the corresponding coradical
ly graded Hopf algebra using an explicit presentation by generators and re
lations of the Nichols algebra.\n\nThe talk is based on a joint work with
Simon Lentner and Guillermo Sanmarco.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell (University of Waterloo\, Canada)
DTSTART:20220728T170000Z
DTEND:20220728T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/85
DESCRIPTION:Title: Recent results on the Dixmier-Moeglin equivalence\nby Jason Be
ll (University of Waterloo\, Canada) as part of LieJor Online Seminar: Alg
ebras\, representations\, and applications\n\n\nAbstract\nDixmier and Moeg
lin showed that if \\(L\\) is a finite-dimensional complex Lie algebra the
n the primitive ideals of the enveloping algebra \\(U(L)\\) are the prime
ideals of \\({\\rm Spec}(U(L))\\) that are locally closed in the Zariski t
opology. 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 complex nu
mbers. Algebras that share this characterization of primitive ideals are s
aid to satisfy the Dixmier-Moeglin equivalence. We give an overview of th
is property and mention some recent work on proving this equivalence holds
for certain classes of twisted homogenous coordinate rings and classes of
Hopf algebras of small Gelfand-Kirillov dimension.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruy Exel (UFSC\, Brazil)
DTSTART:20220804T170000Z
DTEND:20220804T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/86
DESCRIPTION:Title: The opaque ideal\nby Ruy Exel (UFSC\, Brazil) as part of LieJo
r Online Seminar: Algebras\, representations\, and applications\n\n\nAbstr
act\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 tends to
vanish most of the time\, but not always. In the last part of the 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 group on
the 2-sphere used by Banach and Tarski to produce their paradox. This is
based on joint work with David Pitts and Vrej Zarikian.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Sviridova (UnB\, Brazil)
DTSTART:20220714T170000Z
DTEND:20220714T180000Z
DTSTAMP:20260422T213011Z
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\, repr
esentations\, and applications\n\n\nAbstract\nHook theorem is one of the k
ey result of the classical theory of polynomial identities of algebras in
the case of a field of characteristic zero. This well known result is fund
amental for applications of the technique of the classic representation th
eory of the symmetric group to study identities. It has essential connecti
ons with many important facts of PI-theory\, and implies many important an
d interesting consequences. In particular\, it is one of the basic results
for Kemer's positive solution of the Specht problem. Also it is the base
to construct the growth theory for varieties of associative algebras over
a field of of characteristic zero.\n\nIn the last years\, one of the most
popular directions of the theory of polynomial identities is to consider a
lgebras with some additional structures (such as gradings\, involutions\,
actions by automorphisms\, etc.)\, and to study identities of such algebra
s with the additional signature.\n\nWe will discuss the versions of the ho
ok theorem for various types of such identities with complementary structu
res. In particular\, we will represent some version of the hook theorem fo
r identities with some types of actions. This result generalizes the analo
gous results known before\, for example\, for graded identities or identit
ies with involution. We also will discuss some possible consequences and a
pplications of this theorem.\n\nThe talk is based on a joint work with Ren
ata Alves da Silva.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Elduque (Universidad de Zaragoza\, Spain)
DTSTART:20220818T170000Z
DTEND:20220818T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/88
DESCRIPTION:Title: Tensor categories\, algebras\, and superalgebras\nby Alberto E
lduque (Universidad de Zaragoza\, Spain) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nAfter review
ing the basic definitions of tensor categories and the notion of semisimpl
ification of symmetric tensor categories\, it will be shown how the semisi
mplification of the category of representations of the cyclic group of ord
er 3 over a field of characteristic 3 is naturally equivalent to the categ
ory of vector superspaces over this field. This allows to define a superal
gebra starting with any algebra endowed with an order 3 automorphism. As a
noteworthy example\, the exceptional composition superalgebras will be ob
tained\, in a systematic way\, from the split octonion algebra.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Lopatin (UNICAMP\, Brazil)
DTSTART:20220811T170000Z
DTEND:20220811T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/89
DESCRIPTION:Title: Separating invariants for matrices\, octonions and multisymmetric
polynomials\nby Artem Lopatin (UNICAMP\, Brazil) as part of LieJor Onl
ine Seminar: Algebras\, representations\, and applications\n\n\nAbstract\n
In 2002 Derksen and Kemper introduced the notion of separating invariants
as a weaker concept than generating invariants. Roughly speaking\, separat
ing invariants "separate'' exactly the same orbits that are separated by a
ll polynomial invariants. There always exists a finite separating set wher
eas it is not the case for generating invariants. Moreover\, in many cases
separating invariant less depend on the characteristic of the base field
than generating sets. This talk is dedicated to - joint results wi
th Gregor Kemper and Fabian Reimers on separating invariants for the ring
of multisymmetric polynomials in \\(m\\) sets of \\(n\\) variables over an
arbitrary field \\(\\mathbb{F}\\);
- joint results with Alexander Z
ubkov on separating invariants of several octonions with respect to the ac
tion of \\(G_2\\);
- joint results with Felipe Barbosa Cavalcante on
separating invariants of \\(2\\times 2\\) and \\(3\\times 3\\) matrices.<
/ol>\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Petrogradsky (UnB\, Brazil)
DTSTART:20220825T170000Z
DTEND:20220825T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/90
DESCRIPTION:Title: Growth in Lie algebras\nby Victor Petrogradsky (UnB\, Brazil)
as part of LieJor Online Seminar: Algebras\, representations\, and applica
tions\n\n\nAbstract\nDifferent versions of Burnside Problem ask what one can say about finitely generated
periodic groups under additional assumptions. For associative algebras\,
Kurosh type problems ask simila
r questions about properties of finitely generated nil (more generally\, a
lgebraic) algebras. Similarly\, one considers finitely generated restricte
d Lie algebras with a nil \\(p\\)-mapping. Now we study an oscillating intermediate growth in nil restricted Lie algebras.
Name
ly\, for any field of positive characteristic\, we construct a family of 3
-generated restricted Lie algebras of intermediate oscillating growth. We
call them Phoenix algebras\, because of the following.
a) For in
finitely many periods of time the algebra is "almost dying" by having a <
i>quasi-linear growth\, namely the lower Gelfand-Kirillov dimension is
one\, more precisely\, he growth is of type \\(n \\big(\\underbrace{\\ln
\\cdots \\ln}_{q\\ \\text{times}} n\\big )^{\\kappa}\\)\, where \\(q\\in\
\mathbb N\\)\, \\(\\kappa>0\\) are constants.
b) On the other hand\, fo
r infinitely many \\(n\\) the growth function has a rather fast intermedia
te behaviour of type \\(\\exp( n/ (\\ln n)^{\\lambda})\\)\, \\(\\lambda\\)
being a constant determined by characteristic\, for such periods the alge
bra is "resuscitating".
c) Moreover\, the growth function is bounded an
d oscillating between these two types of behaviour.
d) These restricted
Lie algebras have a nil \\(p\\)-mapping.
We also construct nil Lie
superalgebras and nil Jordan superalgebras of similar oscillating interme
diary growth over arbitrary field.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa\, Canada)
DTSTART:20220901T170000Z
DTEND:20220901T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/91
DESCRIPTION:Title: Diagratification\nby Alistair Savage (University of Ottawa\, C
anada) as part of LieJor Online Seminar: Algebras\, representations\, and
applications\n\n\nAbstract\nWe will explain how one can construct diagramm
atic presentations of categories of representations of Lie groups and thei
r associated quantum groups using only a small amount of information about
these categories. To illustrate the technique in concrete terms\, we will
focus on the exceptional Lie group of type F4.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Berele (De Paul University\, USA)
DTSTART:20220922T170000Z
DTEND:20220922T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/92
DESCRIPTION:Title: Poincaré Series of the Trace Rings of Generic Matrices\nby Al
lan Berele (De Paul University\, USA) as part of LieJor Online Seminar: Al
gebras\, representations\, and applications\n\n\nAbstract\nWe first give s
ome background on the Poincare series of the algebra of generic matrices a
nd its associated trace ring\, and then focus on some recent work\, includ
ing a conjecture for the denominator of the one variable series for the tr
ace rings. Time permitting we will also say a bit about traces of direct s
ums.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Facchini (Università degli Studi di Padova\, Italia)
DTSTART:20220929T170000Z
DTEND:20220929T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/93
DESCRIPTION:Title: Multiplicative lattices\, skew braces\nby Alberto Facchini (Un
iversità degli Studi di Padova\, Italia) as part of LieJor Online Seminar
: Algebras\, representations\, and applications\n\n\nAbstract\nThe multipl
icative lattices we will consider are those defined in the paper [3]\, pub
lished in February 2022. Multiplicative lattices yield the natural setting
in which several basic mathematical questions concerning algebraic struct
ures find their answer (Zariski spectrum\, nilpotency\, solvability\, abel
ian algebraic structures\,...) We will consider the particular case of ske
w braces\, which appear in connection to the study of the Yang-Baxter equa
tion ([2]\, [3] and [4]).\n\n[1] D. Bourn\, A. Facchini and M. Pompili\, A
spects of the Category SKB of Skew Braces\, submitted for publication\, av
ailable in arXiv\, 2022\n\n[2] A. Facchini\, Algebraic structures from the
point of view of complete multiplicative lattices\, accepted for publicat
ion in ``Rings\, Quadratic Forms\, and their Applications in Coding Theory
''\, Contemporary Math.\, 2022\, available at: http://arxiv.org/abs/2201.0
3295\n\n[3] A. Facchini\, C. A. Finocchiaro and G. Janelidze\, Abstractly
constructed prime spectra\, Algebra universalis 83(1) (2022).\n\n[4] A. Fa
cchini\, F. de Giovanni and M. Trombetti\, Spectra of Groups\, Algebras Re
p. Theory\, Online first articles published 5 June 2022.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Diniz (Universidade Federal de Campina Grande\, Brazil)
DTSTART:20221117T170000Z
DTEND:20221117T180000Z
DTSTAMP:20260422T213011Z
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\nAbstract\nUppe
r triangular\, and more generally\, block-triangular matrices\, are rather
important in Linear Algebra\, and also in Ring theory\, namely in the the
ory of PI algebras. The group gradings on such algebras have been studied
extensively during the last decades. In 2007 A. Valenti and M. Zaicev con
jectured that every grading on these algebras is obtained from an elementa
ry grading on a block-triangular matrix algebra and a division grading on
a matrix algebra. In this talk we present recent results on this problem.\
n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/95
DESCRIPTION:Title: Simple right-alternative superalgebras\nby Sergey Pchelintsev
and Oleg Shashkov (Financial University under the Government of the Russia
n Federation\, Russia) as part of LieJor Online Seminar: Algebras\, repres
entations\, and applications\n\n\nAbstract\nWe are going to talk about wha
t is known about simple right-alternative superalgebras at this time. Righ
t alternative superalgebras can be divided into two classes\, these are un
ital 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 m
ultiplication of the even part\, which we call the class of singular super
algebras. A scheme of the so-called extended double is given and it is pro
ved that every singular superalgebra is an extended double. The dimensions
for which there are no singular superalgebras are indicated\, and example
s of singular superalgebras of all other dimensions are given.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Nikolov (Oxford University\, UK)
DTSTART:20221006T170000Z
DTEND:20221006T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/96
DESCRIPTION:Title: On conjugacy classes of profinite groups\nby Nikolay Nikolov (
Oxford University\, UK) as part of LieJor Online Seminar: Algebras\, repre
sentations\, and applications\n\n\nAbstract\nIt is well-known that the num
ber of conjugacy classes of a finite group G tends to infinity as the size
of G tends to infinity. There is no such result for a general infinite gr
oup. In this talk I will discuss the situation when G is a profinite group
and show that the number of conjugacy of G is then uncountable unless G i
s finite. The proof depends on many classical results on finite groups and
in particular the classification of the finite simple groups. This is joi
nt work with Andrei Jaikin-Zapirain.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA\, Brazil)
DTSTART:20221013T170000Z
DTEND:20221013T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/97
DESCRIPTION:Title: Higher Fano manifolds\nby Carolina Araujo (IMPA\, Brazil) as p
art of LieJor Online Seminar: Algebras\, representations\, and application
s\n\n\nAbstract\nFano manifolds are complex projective manifolds having po
sitive first Chern class. The positivity condition on the first Chern clas
s has far reaching geometric and arithmetic implications. For instance\, F
ano manifolds are covered by rational curves\, and families of Fano manifo
lds over one dimensional bases always admit holomorphic sections. In recen
t years\, there has been great effort towards defining suitable higher ana
logues of the Fano condition. Higher Fano manifolds are expected to enjoy
stronger versions of several of the nice properties of Fano manifolds. For
instance\, they should be covered by higher dimensional rational varietie
s\, and families of higher Fano manifolds over higher dimensional bases sh
ould admit meromorphic sections (modulo Brauer obstruction). In this talk\
, I will discuss a possible notion of higher Fano manifolds in terms of po
sitivity of higher Chern characters\, and describe special geometric featu
res of these manifolds.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Esteves (IMPA\, Brazil)
DTSTART:20221020T170000Z
DTEND:20221020T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/98
DESCRIPTION:Title: Quiver representations arising from degenerations of linear series
\nby Eduardo Esteves (IMPA\, Brazil) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nWe describe
all the schematic limits of divisors associated to any family of linear se
ries on any one-dimensional family of projective varieties degenerating 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\, ca
lled a Z^n-quiver\, a special representation L of Q in the category of lin
e bundles over X\, called a maximal exact linked net\, and a special subre
presentation V of the representation induced from L by taking global secti
ons\, called a pure exact finitely generated linked net. Given g=(Q\, L\,
V) satisfying these properties\, we prove that the quiver Grassmanian G of
subrepresentations of V of pure dimension 1\, called a linked projective
space\, is Cohen-Macaulay\, reduced and of pure dimension. Furthermore\, w
e prove that there is a morphism from G to the Hilbert scheme of X whose i
mage parameterizes all the schematic limits of divisors along the degenera
ting family of linear series if g arises from one. Joint work with Eduardo
Vital and Renan Santos.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Bartholdi (Saarland University\, Germany)
DTSTART:20221027T170000Z
DTEND:20221027T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/99
DESCRIPTION:Title: Dimension series and homotopy groups of spheres\nby Laurent Ba
rtholdi (Saarland University\, Germany) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nThe lower cen
tral series of a group \\(G\\) is defined by \\(\\gamma_1=G\\) and \\(\\ga
mma_n = [G\,\\gamma_{n-1}]\\). The "dimension series"\, introduced by Magn
us\, is defined using the group algebra over the integers: \\(\\delta_n =
\\{g: g-1\\text{ belongs to the \\(n\\)-th power of the augmentation ideal
}\\}\\).
It has been\, for the last 80 years\, a fundamental proble
m of group theory to relate these two series. One always has \\(\\delta_n\
\ge\\gamma_n\\)\, and a conjecture by Magnus\, with false proofs by Cohn\,
Losey\, etc.\, claims that they coincide; but Rips constructed an exam
ple with \\(\\delta_4/\\gamma_4\\) cyclic of order 2. On the positive side
\, Sjogren showed that \\(\\delta_n/\\gamma_n\\) is always a torsion group
\, of exponent bounded by a function of \\(n\\). Furthermore\, it was beli
eved (and falsely proven by Gupta) that only \\(2\\)-torsion may occur.
In joint work with Roman Mikhailov\, we prove however that every tors
ion abelian group may occur as a quotient \\(\\delta_n/\\gamma_n\\); th
is proves that Sjogren's result is essentially optimal.
Even more i
nterestingly\, we show that this problem is intimately connected to the ho
motopy groups \\(\\pi_n(S^m)\\) of spheres; more precisely\, the quotie
nt \\(\\delta_n/\\gamma_n\\) is related to the difference between homotopy
and homology. We may explicitly produce \\(p\\)-torsion elements starting
from the order-\\(p\\) element in the homotopy group \\(\\pi_{2p}(S^2)\\)
due to Serre.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviane Ribeiro Tomaz da Silva (UFMG\, Brazil)
DTSTART:20221103T170000Z
DTEND:20221103T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/100
DESCRIPTION:Title: On the minimal varieties of PI *-superalgebras and the factorabil
ity of their T-ideals\nby Viviane Ribeiro Tomaz da Silva (UFMG\, Brazi
l) as part of LieJor Online Seminar: Algebras\, representations\, and appl
ications\n\n\nAbstract\nIn this talk\, we deal with varieties of PI-supera
lgebras with graded involution of finite basic rank over a field of charac
teristic zero and we present some recent results concerning the minimality
of these varieties (of fixed *-graded exponent) and the factorability of
their *-graded polynomial identities.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Klep (University of Ljubljana\, Slovenia)
DTSTART:20221110T170000Z
DTEND:20221110T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/101
DESCRIPTION:Title: Factorization of noncommutative polynomials and Nullstellensä
tze for the free algebra\nby Igor Klep (University of Ljubljana\, Slov
enia) as part of LieJor Online Seminar: Algebras\, representations\, and a
pplications\n\n\nAbstract\nThe singularity set of a noncommutative polynom
ial \\(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 results wi
ll be presented. Firstly\, irreducible factors of \\(f\\) are shown to be
in a natural bijective correspondence with irreducible components of \\(Z_
n(f)\\) for every sufficiently large \\(n\\). In particular\, \\(f\\) is i
rreducible if and only if \\(Z_n(f)\\) is eventually irreducible. Secondly
\, we give Nullstellensätze for noncommutative polynomials. For instan
ce\, 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 polynomials will
be presented.
The talk is based on joint works with Jurij Vol
9ič and Bill Helton.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University\, USA)
DTSTART:20221208T170000Z
DTEND:20221208T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/102
DESCRIPTION:Title: An operadic approach to vertex algebras and Poisson vertex algebr
as\nby Bojko Bakalov (North Carolina State University\, USA) as part o
f LieJor Online Seminar: Algebras\, representations\, and applications\n\n
\nAbstract\nI will start by reviewing the notions of vertex algebra\, Pois
son vertex algebra\, and Lie conformal algebra\, and their relations to ea
ch other. Then I will present a unified approach to all these algebras as
Lie algebras in certain pseudo-tensor categories\, or equivalently\, as mo
rphisms 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 Poisson ve
rtex algebras and of Lie conformal algebras. The talk is based on joint wo
rk with Alberto De Sole\, Reimundo Heluani\, Victor Kac\, and Veronica Vig
noli.\n
LOCATION:https://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:20260422T213011Z
UID:LieJor_Seminar/103
DESCRIPTION:Title: Improvements of the Noether bound for polynomial invariants of fi
nite groups\nby Matyas Domokos (Renyu Institute of Mathematics\, Budap
est\, Hungary) as part of LieJor Online Seminar: Algebras\, representation
s\, and applications\n\n\nAbstract\nGiven a field and a finite group G\, t
he Noether number of G is defined as the minimal positive integer d such t
hat for any finite dimensional G-module V\, the algebra of G-invariant pol
ynomial functions on V is generated by elements of degree at most d. In th
e talk we shall survey results (obtained mostly together with Kálmán Czi
szter) on the Noether number of various finite groups.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Zalesski (UnB\, Brazil)
DTSTART:20221215T170000Z
DTEND:20221215T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/104
DESCRIPTION:Title: Combinatorial theory of pro-p groups\nby Pavel Zalesski (UnB\
, Brazil) as part of LieJor Online Seminar: Algebras\, representations\, a
nd applications\n\n\nAbstract\nFree product with amalgamation and HNN-exte
nsion are two main constructions of combinatorial group theory. I shall di
scuss these two constructions in the category of pro-\\(p\\) groups\, pres
enting results on splittings of pro-\\(p\\) groups as an amalgamated free
pro-\\(p\\) product or a pro-\\(p\\) HNN-extension and relating them with
pro-\\(p\\) version of Bass-Serre's theory of groups acting on trees. I s
hall also compare the pro-\\(p\\) results with similar results for abstra
ct groups.\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Yasumura (IME-USP\, Brazil)
DTSTART:20221201T170000Z
DTEND:20221201T180000Z
DTSTAMP:20260422T213011Z
UID:LieJor_Seminar/105
DESCRIPTION:Title: Group gradings on the infinite dimensional triangular algebra
\nby Felipe Yasumura (IME-USP\, Brazil) as part of LieJor Online Seminar:
Algebras\, representations\, and applications\n\n\nAbstract\nIn the last d
ecades\, there has been an increasing interest in the classification of is
omorphism classes of group gradings on a given algebra. We discuss some di
fficulties concerning the study of group gradings on infinite-dimensional
algebras. Then\, we present our results on the classification of the gradi
ngs on the infinite-dimensional triangular algebra. This is joint work wit
h Waldeck Schutzer (UFSCar).\n
LOCATION:https://researchseminars.org/talk/LieJor_Seminar/105/
END:VEVENT
END:VCALENDAR