Special Topics 581C: Lie algebras

Instructor: Julia Pevtsova

Place: Loew Hall, 219

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.

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

2. Homework 2

3. Homework 3

Lecture Notes for the Snow closure on November 24: Cartan Matrices and Dynkin diagrams

End of quarter presentation assignments; to be presented the week of Nov. 29 (after Thanksgiving):

1. Classification of Coxeter graphs: Chad, Trevor, (possibly Kevin and Andrew)

Existence:

· A_n Amy and Camil

· B_n and C_n Cody and Luke

· D_n Brendan and Cris

· E₈ (and E_6, E₇) Gautam and Xingting

· F₄ David and Jim