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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Groups and Representations

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Code Completion Credits Range Language
02GR Z,ZK 3 2+1 Czech
Lecturer:
Lenka Motlochová, Goce Chadzitaskos (guarantor)
Tutor:
Lenka Motlochová, Goce Chadzitaskos (guarantor)
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 2018/2019:
Time-table is not available yet
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-03-19
For updated information see http://bilakniha.cvut.cz/en/predmet24532105.html