**Algebraic Structures 507A: Lie algebras
**

__Instructor__: Julia
Pevtsova

__Place__: Padelford, C-401

__Time__: 9:30-10:20, MWF

__Office Hours__: by
appointment (that is, I am happy to talk between classes, just need an advance
notice)

Course Description. An introductory course on Lie algebras and their representations. Topics to be covered: Enveloping Algebras and PBW theorem, root systems, classification of simple Lie algebras, representations.

__Grading system__. Based on homework and presentations.

__Textbook__. J. Humphreys, *Introduction
to Lie Algebras and Representation Theory*

Other references:

·
Jacques Dixmier, *Enveloping algebras*

·
N. Jacobson*,
Lie algebras*

·
N. Jacobson*,
Exceptional Lie algebras*

·
J. Humphreys, *Reflection groups and Coxeter groups*

·
A.A. Kirillov*, An Introduction to Lie Groups and Lie
Algebras*

·
J.P. Serre, *Complex semisimple
Lie algebras*

Homework assignments.

1. Homework 1. Tex. Due Friday, October 21.

2. Homework 2. Tex. Due Monday, November 28

End of quarter presentation assignments; to be presented the week of Nov. 28 (after Thanksgiving), on the general topic of classification of Coxeter graphs. TBD.