Introduction to Kac–Moody algebras
This is a continuation of two Lie algebra course in 2025; see https://bimsa.net/activity/InttoLiealg/ and https://bimsa.net/activity/InttoLiealgII/ for previous notes and recordings. We will follow the Carter text and start from Chapter 14.
Kac-Moody algebras can be viewed as a generalization of finite-dimensional simple Lie algebras. Many notions and results from finite-dimensional Lie algebras extend to Kac-Moody algebras. This includes (generalised) Cartan matrix, root system, Weyl group, weight lattice, representation by dominant weights, Weyl character formula, etc. We will mainly focus on affine Kac-Moody algebras as well as their realizations and representations.
This course should be useful for people interested in Lie theory, quantum algebras, or representation theory. Kac-Moody algebras have applications in combinatorics, topology, geometry, number theory, string theory, conformal field theory, and many others.
Kac-Moody algebras can be viewed as a generalization of finite-dimensional simple Lie algebras. Many notions and results from finite-dimensional Lie algebras extend to Kac-Moody algebras. This includes (generalised) Cartan matrix, root system, Weyl group, weight lattice, representation by dominant weights, Weyl character formula, etc. We will mainly focus on affine Kac-Moody algebras as well as their realizations and representations.
This course should be useful for people interested in Lie theory, quantum algebras, or representation theory. Kac-Moody algebras have applications in combinatorics, topology, geometry, number theory, string theory, conformal field theory, and many others.
讲师
日期
2026年04月02日 至 06月18日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四 | 13:30 - 16:55 | A3-1-101 | ZOOM B | 462 110 5973 | BIMSA |
修课要求
Basic Lie algebras and their representations (Chapters 1-13 of the Carter text).
课程大纲
14 Generalised Cartan matrices and Kac–Moody algebras
15 The classification of generalised Cartan matrices
16 The invariant form, Weyl group and root system
17 Kac–Moody algebras of affine type
18 Realisations of affine Kac–Moody algebras
19 Some representations of symmetrisable Kac–Moody algebras
20 Representations of affine Kac–Moody algebras
21 Borcherds Lie algebras
15 The classification of generalised Cartan matrices
16 The invariant form, Weyl group and root system
17 Kac–Moody algebras of affine type
18 Realisations of affine Kac–Moody algebras
19 Some representations of symmetrisable Kac–Moody algebras
20 Representations of affine Kac–Moody algebras
21 Borcherds Lie algebras
参考资料
Roger Carter. Lie algebras of finite and affine type. Cambridge U. Press, 2005.
Victor Kac. Infinite Dimensional Lie Algebras. Cambridge U. Press, 1990.
Victor Kac. Infinite Dimensional Lie Algebras. Cambridge U. Press, 1990.
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