Group theory II

  Teacher:  Professor You-Quan Li

2008-2009 semester

     The main purpose of this course is to provide for graduated students whose major are "theoretical condensed matter physics" or "theoretical physics" the essential  knowledge of group theory and useful techniques applicable for solving physics problems. 

Tentative contents  (Group Theory II is the continued contents of Group Theory I)

I. Basic Concepts

1. Introductory Concepts

II. Discrete Groups      

2. Finite Group Related to Symmetries in Physics

    [Crystallographic space group  (tables)  Point group symmetry  Crystal lattice structures]

3. Application Examples

4. Permutation Group, Braid Group and Knot theory

III. Continuous Groups

5. The Classical Group: Group of Transformation 

6. Lie Groups

7. Lie Groups and Lie Algebras

8. Topological Properties of Lie  Groups

9. Root Space and Dynkin Diagrams

10. Weight Space and Representations

IV* Advanced Topics

11. Affine Lie Algebras

12. Quantum Groups and Noncommutative Geometry

References

R. Gilmore, Lie Group, Lie Algebra and Some of Their Applications, (Dover Publications) .

R.N. Cahn, Simple Lie Algebras and their Representations.

G. Racah, Group theory and spectroscopy.

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