Representations and characters of groups
著者
書誌事項
Representations and characters of groups
（Cambridge mathematical textbooks）
Cambridge University Press, 1993
- : hbk
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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