SYLLABUS / SCHEDULE
Course Overview
| Lecture 1, 2: | Introduction, basic definitions |
| Lecture 3-5: | Engel and Lie theorems |
| Lecture 6-9: | Cartan subalgebras and Cartan's criterion |
| Lecture 10: | Conjugacy of Cartan subalgebras |
| Lecture 11-14: | Structure of semi-simple Lie algebras |
| Lecture 15-20: | Classification of simple Lie algebras |
| Lecture 21: | Compact form and Weyl group |
| Lecture 22: | Universal enveloping algebra, PBW theorem, Casimir element and cohomology of Lie algebras |
| Lecture 23: | Weyl, Levi and Maltsev theorems |
| Lecture 24: | Verma modules |
| Lecture 25, 26: | Finite-dimesional representations of semisimple Lie algebras. Weyl character and dimension formulae |
Recommended Books
- J.P. Serre, "Complex Semi Simple Lie Algebras"
- J.E. Humphreys, "Introduction to Lie Algebras and Representation Theory"
- A.L. Onishchik, E.B. Vinberg, "Lie Groups and Algebraic Groups"
Course Requirements
- Typing tow lectures (using TeX is preferred, MS Word is ok; contact typers of previous lectures of templates). Lecture notes should be handed in within two weeks of the date of the lecture.
- Doing exercises given in the course of lecture; collected and graded weekly. The exercises from the previous two lectures are due every Tuesday (if holiday, then the next Tuesday).
