Lie Algebras and Representation Theory
Spring 2007 Math 690A
Instructor: Richard Ng
Office:
Carver Hall 466
Phone:
515-294-1016
E-mail:
rng@iastate.edu
Homepage: http://www.math.iastate.edu/rng
Class: T
3:10pm-4pm and H 3:10pm-5pm
(Carver 032) Click here for
homework assignments
Objective: Lie algebras and their representations have been useful in many important areas of mathematics and physics. The classification of complex simple Lie algebras via Dynkin diagrams is elegant and elementary. The topic course provides an introduction to Lie algebras and, in particular, the classification of complex semisimple Lie algebras.
Textbook: James Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9. Springer-Verlag, New York-Heidelberg, 1978.
Course description and Topics: The course will start with an introduction to Lie algebras and their representations, and then specialize to the discussion of semisimple Lie algebras over complex field and their classification.
The class will be self-contained and the following topics are considered to be covered:
- Basic concepts on Lie algebra
- Semisimple Lie algebras
- Root Systems and the classification of simple Lie algebras
- Isomorphism and Conjugacy Theorems
- Universal enveloping algebras and Poincare-Birkhoff-Witt Theorem
Grading: The grade is based on homework assignments or presentations.
