Introduction to Lie algebras
This is a basic course on Lie algebras, designed to be self-contained. We will follow the Carter text and cover Chapters 1-8. We will be learning the basic topics in the theory of Lie algebras, such as: solvable and nilpotent Lie algebras, Cartan subalgebras, the Cartan decomposition, semisimple Lie algebras, the Killing form, the root system, the Weyl group, Dynkin diagrams, Cartan matrices.
Our main goal is to learn and prove the classification of the finite-dimensional semisimple Lie algebras over the complex numbers, up to isomorphism.
For people interested in Lie theory, quantum groups, algebraic combinatorics, number theory, or special functions, this course should help in building the foundation.
Our main goal is to learn and prove the classification of the finite-dimensional semisimple Lie algebras over the complex numbers, up to isomorphism.
For people interested in Lie theory, quantum groups, algebraic combinatorics, number theory, or special functions, this course should help in building the foundation.
Lecturer
Date
4th March ~ 21st May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 15:20 - 16:55 | A3-1a-204 | ZOOM 04 | 482 240 1589 | BIMSA |
| Wednesday | 10:40 - 12:15 | A3-1a-204 | ZOOM 04 | 482 240 1589 | BIMSA |
Prerequisite
Linear algebra
Syllabus
1 Basic concepts
2 Representations of soluble and nilpotent Lie algebras
3 Cartan subalgebras
4 The Cartan decomposition
5 The root system and the Weyl group
6 The Cartan matrix and the Dynkin diagram
7 The existence and uniqueness theorems
8 The simple Lie algebras
2 Representations of soluble and nilpotent Lie algebras
3 Cartan subalgebras
4 The Cartan decomposition
5 The root system and the Weyl group
6 The Cartan matrix and the Dynkin diagram
7 The existence and uniqueness theorems
8 The simple Lie algebras
Reference
Main text:
Roger Carter. Lie algebras of finite and affine type. Cambridge U. Press, 2005.
The Carter text does not contain exercises. You can find exercises in these supplemental texts:
J. Humphreys. Introduction to Lie algebras and representation theory.
W. Fulton and J. Harris. Representation theory, a first course.
Roger Carter. Lie algebras of finite and affine type. Cambridge U. Press, 2005.
The Carter text does not contain exercises. You can find exercises in these supplemental texts:
J. Humphreys. Introduction to Lie algebras and representation theory.
W. Fulton and J. Harris. Representation theory, a first course.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
English