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.