报告题目：Finite-dimensional Lie algebras  

报 告 人：Maxim Goncharov

所在单位：Sobolev Institute of Mathematics

报告时间：July 22-31, 2025, 15:30-16:30

报告地点：Zoom Id: 904 645 6677，Password: 2024

会议链接：

//zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

报告摘要: 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:

1. Definition and basic examples of Lie algebras.

2. Ideals, homomorphisms, automorphisms, and derivations of Lie algebras.

3. Solvability and nilpotency of Lie algebras. Engel's theorem.

4. Jordan-Chevalley decomposition, Cartan's Criterion for Solvability.  

5. Killing form, semisimple Lie algebras.

6. Representations and modules of Lie algebras. Schur's Lemma.

7. Weyl's theorem.

8. Universal enveloping algebra. PBW theorem.

报告人简介： Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.