Instructor: Professor Victor Kac
Email: kac [at] math . mit .edu
Office: Room 2-176
Office Hours: By Appointment
Grader: Gurbir Dhillon email@example.com
Lectures: TR 2:30-4:00 2-143
|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|
- 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"
- 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