Introduction to Lie algebras II
This is a continuation of the Lie algebra course in Spring 2025. We will follow the Carter text and cover Chapters 9-13. Keywords: universal enveloping algebra, PBW basis, Verma module, Casimir element, character formula, dimension formula, fundamental module. This course should be useful for people interested in Lie theory, quantum algebras, algebraic combinatorics, number theory, or special functions.
讲师
日期
2025年10月13日 至 12月30日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周二 | 10:40 - 12:15 | A3-1-301 | ZOOM 14 | 712 322 9571 | BIMSA |
修课要求
The basic theory of finite-dimensional semisimple Lie algebras, in particular their classification in terms of the Cartan matrices/Dynkin diagrams (first 8 chapters of the Carter text).
课程大纲
9 Some universal constructions
10 Irreducible modules for semisimple Lie algebras
11 Further properties of the universal enveloping algebra
12 Character and dimension formulae
13 Fundamental modules for simple Lie algebras
10 Irreducible modules for semisimple Lie algebras
11 Further properties of the universal enveloping algebra
12 Character and dimension formulae
13 Fundamental modules for simple Lie algebras
参考资料
Roger Carter. Lie algebras of finite and affine type. Cambridge U. Press, 2005.
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
视频公开
公开
笔记公开
公开
语言
英文