Math 427: Lie groups

Basic Information


Mathematics 423 or consent of instructor.

If you have any questions or concerns, please contact me by e-mail.

Course outline

This course is an introduction to Lie theory. The first part of the course will cover the foundations:

The remainder of the course will touch on the following topics:

Abelian, nilpotent, solvable and semi-simple Lie groups, Levi decomposition, semi-direct products. Compact Lie groups, Peter-Weyl theorem, maximal tori, Weyl groups. Ado's theorem: every finite dimensional Lie algebra is a matrix Lie algebra. Cartan's theorem (Lie's third theorem): every finite dimensional Lie algebra is a Lie algebra of a Lie group.


The official text is Lie groups beyond an introduction by A. W. Knapp
There is also a recommended text:


The course grade will be based on homework. Homework will be assigned weekly. One problem per homework will be graded.
Last modified: Tue Aug 24 13:51:30 CDT