Course No.：S070100ZJ005
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Calculus, Linear algebra
Aims & Requirements：
This course provides an introduction to Lie groups, Lie algebras and representations theory, aimed at graduate students in mathematics and physics.
The theory of Lie groups plays a fundamental role in many areas of mathematics. The structure of complex Lie algebras is discussed. The heart of the course is a fairly complete treament of the fine structure of complex semisimple Lie algebras.
Primary Coverage
Chapter 1 General Theory
Real Lie Groups; Complex Lie Groups; Lie algebras; Lie subalgebras; Ideals; Quotient algebras; Simple algebras.
Chapter 2 Structure of Complex algebras
Nilpotent algebras; Weights; Cartan subalgebras; Cartan decomposition; Conjugate Theorem.
Chapter 3 Classification of Complex Semisimple algebras;
Root system; Simple Root system; Dynkin diagram; Classification Theorem.
Chapter 4 Compact Real forms
Real forms; Weyl basis; Chevalley basis; Compact Real forms.
References:
1. Z.X. Wan，Lie algebras, Science Press, Beijing, 1964.
2. B.C. Hall, Lie Groups, Lie Algebras, and Representations, GTM 222. Springer (2003)。
3. D.J. Meng, Introduction to Complex SemisimpleLie Algebra, Beijing University
Press, 1998.
Author: Liang Xiao（Mathematical School of GUCAS）
Date： Apiril,2012
