Math 5032 Algebra II

Instructor : Yanli Song

Suggested Textbook:

A. Lie groups, Lie algebras and representations (Hall)

B. Compact Lie groups (Sepanski) (B)

C. Introduction to Lie Groups and Lie Algebras (Kirillov)

D. Matrix Groups: An introduction to Lie group theory (Baker).

Office Hour:

Cupples I 116, Wed 11-12, Monday 11-12 or by appointment.

Course outlime:

Representation of compact matrix groups.

Grading policy :

Homework 20%+ Presentation 40% + Final 40%.

Homework :

Homework 1

Homework 2

Homework 3

Practice Problems (keep updating)

Project problems

SU(3) representation

Weekly topics :

1. Examples of matrix groups
Book A, Chapter 1 and Book D, Chapter 1

2. Exponential maps and Lie algebras
Book A, Chapter 2 and Book D, Chapter 2&3

3. Maximal torus and maximal abelian subalgebras

4. Schur's lemma, Character of representations.

5. Representation of SU(2)

5. Representation of SU(3)

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