An online session of the Algebra and Logic Seminar will be held on April 1, 2022 (Friday) at 1:00 pm (UTC+3).

A talk on:

Automorphisms of simple quotients of the Poisson and universal enveloping algebras of sl_2

will be delivered by Altyngul Naurazbekova (L. N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan).

Abstract. Let P(sl_2(K)) be the Poisson enveloping algebra of the Lie algebra sl_2(K) over an algebraically closed field K of characteristic zero. U. Umirbaev, V. Zhelyabin proved that the quotient algebras P(sl_2(K))/(C_P – λ), where C_P is the standard Casimir element of sl_2(K) in P(sl_2(K)) and 0 ≠ λ ∈K, are simple. Using a result by L. Makar-Limanov on groups of automorphisms of a class of surfaces, we describe generators of the automorphism group of P(sl_2(K))/(C_P – λ) and represent this group as an amalgamated product of its subgroups. Moreover, using similar results by J. Dixmier and O. Fleury for the quotient algebras U(sl_2(K))/(C_U – λ), where C_U is the standard Casimir element of sl_2(K) in the universal enveloping algebra U(sl_2(K)), we prove that the automorphism groups of P(sl_2(K))/(C_P – λ) and U(sl_2(K))/(C_U – λ) are isomorphic.

This is a joint work with professor U. Umirbaev.

The seminar will be held via Zoom and anyone can join at:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Apr 1, 2022 01:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647

Algebra and Logic Department, IMI-BAS
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================