Groups and Representations

Lecturer:

Goce Chadzitaskos (gar.)

Tutor:

Goce Chadzitaskos (gar.)

Supervisor:

Department of Physics

Synopsis:

The lecture course is dedicated to the introduction to the group theory and group representations including their applications in physics.

Requirements:

None

Syllabus of lectures:

1. Symmetry in physics and its mathematical realization.

2. Basic definitions.

3. Group action.

4. Introduction to the theory of moduls.

5. Schur's lemma, group algebra.

6. Group representations, ireducibility, Maschke's theorem.

7. Complex representations.

8. Characters, orthogonality.

9. Character tables.

10. Symmetry in quantum mechanics.

11. Group representations in Hilbert spaces.

12. Symmetric and braid groups.

Syllabus of tutorials:

Semigroups. groups, rings

Classificatioin of groups of different order

Representations of groups

Study Objective:

Knowledge: become acquainted with the methods of classification of discrete groups and their representations.

Abilities: classify of the groups of some order

Study materials:

Key reference

[1] H. F. Jones: „ Groups, Representations and Physics“, 2nd Ed., IOP, Bristol 1998.

Recommended references

[2] D.S, Dummit, R.M.Foote: Abstract Algebra, John Wiley and Sons, 2004,

[3] C. W. Curtis and I. Reiner: „Representation Theory of Finite Groups and Associative Algebras“, John Wiley and Sons, NY 1962.

[4] I. M. Isaacs: „Character Theory of Finite Groups“, Dover, NY 1976.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: