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Lie Groups and Lie Algebras

920

General properties of Lie groups, closed subgroups, one-parameter subgroups, homogeneous spaces, Lie bracket, Lie algebras, exponential map, structure of semi-simple Lie algebras, invariant forms, Maurer-Cartan equation, covering groups, spinor groups.

Text: 

No Text.

Prerequisite: 

MATH 766 and MATH 790 and MATH 791.

Credit Hours: 
3

This course is an introduction to the fundamentals of Lie groups and Lie algebras, including the following topics: Lie groups, closed subgroups, one-parameter subgroups, homogeneous spaces, Lie bracket, Lie algebras, exponential map, invariant forms, Maurer-Cartan equation, semi-simple Lie algebras, Cartan subalgebra, root system, Dynkin diagram, representation theory, universal covering group, etc.

(Sheu 2012 )

Frequency: 
Irregularly

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