Representations and characters of groups
Author(s)
Bibliographic Information
Representations and characters of groups
（Cambridge mathematical textbooks）
Cambridge University Press, 2001
2nd ed
- : pbk
- : hbk
Available at / 37 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
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. Character table of GL(2,q)
- 29. Permutations and characters
- 30. Applications to group theory
- 31. Burnside's theorem
- 32. An application of representation theory to molecular vibration.
by "Nielsen BookData"