18.745 - Introduction to Lie Algebras (Fall 2010)


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

Course Requirements