Program
Introduction to Lie groups and transformation groups
Student No.:50
Time:Mon/Tue13:00-14:50, 2014-06-17 ~ 2014-08-19
Instructor:Lizhen Ji  [University of Michigan]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2014-6-17
Ending Date:2014-8-19

 

 

Description:

 

 

 

 

In this course, we will give an introduction to Lie groups, Lie algebras with some emphasis on linear Lie groups.
We will also discuss actions of Lie groups, in particular of compact Lie groups on smooth manifolds. Actions of Lie groups arise from many applications of Lie groups, and they are also crucial to understanding structures of Lie groups.

For example, homogeneous spaces, symmetric spaces and locally symmetric spaces are all quotients of group actions, the adjoint action of a Lie group on itself is crucial to understanding structure and properties of the Lie group.

 

Reference:

 

Basically, we will follow the topics in the following two books:
 
Brian Hall,
Lie groups, Lie algebras, and representations.
An elementary introduction.
Graduate Texts in Mathematics, 222. Springer-Verlag, New York, 2003. xiv+351 pp.
 
J. Duistermaat, J. Kolk,
Lie groups.
Universitext. Springer-Verlag, Berlin, 2000. viii+344 pp.