Lie Group, Lie Algebras and Representations Theory

  • 申立勇
  • Created: 2014-12-08
Lie Group, Lie Algebras and Representations Theory


Course No.S070100ZJ005    

Course CategoryProfessional Basic Course         


PrerequisitesCalculus, 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.


1. Z.X. WanLie 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 XiaoMathematical School of GUCAS

Date Apiril,2012