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.
Lecturer
Date
13th October ~ 30th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Tuesday | 10:40 - 12:15 | A3-1-301 | ZOOM 14 | 712 322 9571 | BIMSA |
Prerequisite
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).
Syllabus
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
Reference
Roger Carter. Lie algebras of finite and affine type. Cambridge U. Press, 2005.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
Video Public
Yes
Notes Public
Yes
Language
English