Vyacheslav Futorny (USP), Jonas Gonçalves Lopes (UFRN)
Abstract: we shall discuss the properties of normalizers
of finitely generated subgroups of the profinite
completion of a virtually free group and their implications for conjugacy separability.
Abstract: We will discuss the relations of graded and
non-graded identities of some Z_2-graded associative algebras.
We study some interesting Z_2-graded identities of associative algebras and the
algebras satisfying them. We find some non-graded consequences and will discuss
their possible relations with other algebraic objects.
Abstract: We will talk about general properties of
algebras of polynomial integro-differential
operators. Their groups of automorphisms are found. Apart of the case of one variable (Dixmier 1968), the groups of automorphisms
of polynomial differential operators (i.e. the Weyl
algebras) are wide open.
Abstract: We discuss analogues of group theoretic constructions
for Lie algebras. We consider groups acting on trees and explain why their analogs are Lie algebras
acting by differential operators. Such analogies are better understood using Hopf algebra theory.
Abstract: We
will present definitions of differential operators, and their beta and quantum analogues,
as given by Lunts and Rosenberg. We then present
several concrete examples.
Abstract: We
describe the twisted Ringel-Hall algebra of bound
quivers with small homological dimension. The description is given in the terms
of quadratic form associated with the corresponding bound quiver.
Abstract: For some singular Gelfand-Tsetlin
characters we present an explicit construction of a universal module M with a
tableaux-like realization generalizing classical Gelfand-Tsetlin
formulas.
Abstract: Glauberman,
Doro and Mikheev established a connection between Moufang loops and groups with automorphisms
of special type (groups with triality). This
connection turns out to be very useful for the studying of the properties of Moufang loops. In particular, it was used by M.W. Liebeck for the classification of simple finite Moufang loops and by A.N. Grishkov
and A.V. Zavarnitsine in their proof of an analogue
of Lagrange's theorem for finite Moufang loops. A
similar connection between Malcev algebras and Lie
algebras with triality was obtained by P.O. Mikheev. A.N. Grishkov showed
that using this connection some principal results in the theory of Malcev algebras may be obtained as consequences of similar
results for Lie algebras. Let (A,Δ) be a coalgebra. If the dual algebra A* is a Lie (Malcev) algebra then the pair (A,Δ) is called
Lie (Malcev) coalgebra. In
this work we establish a connection between Malcev coalgebras and Lie coalgebras
having automorphisms of a special type (Lie coalgebras with triality).