Representations and Characters of Groups
Representations and Characters of Groups
Martin W. Liebeck, Imperial College of Science, Technology and Medicine, London
This book provides a modern introduction to the representation theory of finite groups. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Amongst those applications covered are Burnside's paqb theorem, the use of character theory in studying subgroup structure, and a description of how to use representation theory to investigate molecular vibration. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book. This will be suitable as a text for those teaching a course in representation theory, and in view of the applications of the subject, will be of interest to chemists and physicists as well as mathematicians.
- Based on course given by authors
- Material is broken down into bite-sized chapters
- Some of the material has applications to chemistry and physics
Product details
No date availablePaperback
9780521445900
429 pages
226 × 150 × 28 mm
0.689kg
Table of Contents
- 1. Groups and homomorphisms
- 2. Vector spaces and linear transformations
- 3. Group representations
- 4. FG-modules
- 5. FG-submodules
- 6. Group algebras
- 7. FG-homomorphisms
- 8. Mashcke's theorem
- 9. Schur's lemma
- 10. Irreducible modules and the group algebra
- 11. More on the group algebra
- 12. Conjugacy classes
- 13. Characters
- 14. Inner products of characters
- 15. The number of irreducible characters
- 16. Character tables and orthogonality relations
- 17. Normal subgroups and lifted characters
- 18. Some elementary character tables
- 19. Tensor products
- 20. Restriction to a subgroup
- 21. Induced modules and characters
- 22. Algebraic integers
- 23. Real representations
- 24. Summary of properties of character tables
- 25. Characters of groups of order pq
- 26. Characters of some p-groups
- 27. Character table of the simple group of order 168
- 28. An application to group theory
- 29. Burnside's theorem
- 30. An application of representation theory to molecular vibration.
