Title: Finite-dimensional Lie algebras
Speaker: Maxim Goncharov
Affiliation: Sobolev Institute of Mathematics
Time: July 23-26, 27-31, 2025, 15:30-16:30
Venue: Zoom ID: 814 1002 3263, Password: 2025
Meeting Link:
https://us06web.zoom.us/j/81410023263?pwd=0ysq272PCzQqZjuOoLJTvbwV99Xub2.1
Abstract:
In this lecture course, we will focus on the basic theory of finite-dimensional Lie algebras over an algebraically closed field of characteristic 0. We will discuss main notions and constructions (derivations, the Radical, Killing form, and the universal enveloping algebra) and classical results (such as Engel's theorem, Cartan's Criterion, and Weyl's theorem) in the theory of Lie algebras. Also, we will consider some exercises to illustrate the theory and gain practical experience. The minicourse is organized as follows:
Definition and basic examples of Lie algebras.
Ideals, homomorphisms, automorphisms, and derivations of Lie algebras.
Solvability and nilpotency of Lie algebras. Engel's theorem.
Jordan-Chevalley decomposition, Cartan's Criterion for Solvability.
Killing form, semisimple Lie algebras.
Representations and modules of Lie algebras. Schur's Lemma.
Weyl's theorem.
Universal enveloping algebra. PBW theorem.
Speaker's Biography:
Maxim Goncharov, Ph.D., is a Senior Research Fellow at the Sobolev Institute of Mathematics and an Associate Professor at Novosibirsk State University.
