mp.weixin.qq.com/s/kDbnM9fnAUyMC36wu7YfiQ
Finite-dimensional Lie algebras
报告人/Speaker
Maxim Goncharov (Sobolev Institute of Mathematics)
报告时间/Time
2025年7月23日-26日，27日-31日
15:30-16:30
报告地点/Venue
Zoom ID: 904 645 6677，Password: 2024
会议链接/Link
报告摘要/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:
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.
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FROM 202.120.11.*