RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 Forthcoming seminars Seminar calendar List of seminars Archive by years Register a seminar Search RSS Forthcoming seminars

You may need the following programs to see the files

Algebras in Analysis
September 28, 2018 18:05–19:35, Moscow, Lomonosov Moscow State University, room 13-20.

Universal enveloping algebras, analytic functionals, and homological epimorphisms

O. Yu. Aristov

Abstract: We discuss homological properties of the algebra $\mathcal A(G)$ of analytic functionals on a complex Lie group $G$. We show that
(1) If $G$ is linearly complex reductive (for example, semisimple) and connected, then $\mathcal A(G)$ is homologically trivial.
(2) For each connected $G$ the Arens-Mchael envelope of $\mathcal A(G)$ is a homological epimorphism.
As a corollary, the solvability of a finite-dimensional complex Lie algebra $\mathfrak g$ is sufficient for the Arens-Michael envelope of the enveloping algebra $U(\mathfrak g)$ to be a homological epimorphism. (Pirkovskii proved earlier that this condition is necessary.)