Instructor: Professor Victor Kac
Email: kac [at] math . mit .edu
Office: Room 2-176
Office Hours: By Appointment
Grader: Gurbir Dhillon gdhillon@mit.edu
Lectures: TR 2:30-4:00 2-143
COURSE OVERVIEW
| Lecture 1, 2: | Introduction, basic definitions |
| Lecture 3-5: | Engel and Lie theorems |
| Lecture 6-9: | Cartan subalgebras and Chevally's conjugacy theorem |
| Lecture 10: | Cartan's criterion |
| Lecture 11-14: | Structure of semi-simple Lie algebras |
| Lecture 15-20: | Classification and construction 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-dimensional 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 two lectures ( using TeX is preferred, MS Word is ok; contact typers of previous lectures for templates). Lecture notes should be handed in within a week 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).
- No final exam