18.745 - Introduction to Lie Algebras (Fall 2010)

Instructor: Victor Kac

Office: Room 2-178

Email: kac@math.mit.edu

Grader: John Ullman

Office: Room 2-489 (4-1348)

Lectures: T R 2:30 - 4:00 pm 2-136

Office Hours: Tuesdays 4:30 pm in 2-178

COURSE DESCRIPTION

Structure of finite-dimensional Lie algebras. Theorems of Engel and Lie. Cartan subalgebras and regular elements. Trace form and Cartan's criterion. Chevalley's conjugacy theorem. Classification and construction of semisimple Lie algebras. Weyl group. Universal enveloping algebra and the Casimir operator. Weyl's complete reducibility theorem, Levi and Maltsev theorems. Verma modules. Classification of irreducible finite-dimensional representations of semisimple Lie algebras. Weyl's character and dimension formulas.

Prerequisites: 18.701 or 18.703

Instructions for Writing Notes

If you are writing notes and exercises send them to Professor Kac in tex form. After he has approved the notes, email them to me in tex and pdf format. My email address is willst@mit.edu. If you have any issues or questions with the website please email me as well.

The template sent out by Professor Kac is below

LaTeX Template

Here is a schedule of who is responsable for notes for each lecture.

Schedule

Please email me the exercises seperatly from the notes if possible. Then they can appear under Weekly Exercises for easy access.