Representations and Characters of Groups
2nd Edition
Published on 18. October 2001
Book
Hardback
468 pages
978-0-521-81205-4 (ISBN)
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.
Reviews / Votes
'... this reviewer regards the second printing of the book as a gem in studying representation theory of finite groups.' R. W. van der Wall, Zentralblatt fuer Mathematik 'This is a beautiful well-balanced introduction to representations and characters of finite groups over the complex field, suitable for advanced undergraduate and beginning graduate students. The reviewer enjoyed the exposition tremendously and strongly recommends this already popular book both as a textbook and for self-study.' EMS 'For me, the attractive features are the short chapters (substantial but bite-sized), the motivational comments throughout the book and useful summaries at the end of each chapter, the wealth of detailed examples which break up and illuminate the theory, and full solutions to all the exercises.' The Mathematical Gazette 'The review found this to be a clearly and carefully written book, which he will recommend to all students seeking an introduction to group representation theory. the authors write in a down-to-earth style, provide a large number of examples throughout, and give very useful content summaries at the end of each chapter ... In summary, the additions to the second edition only improve what was already an excellent text.' Proceedings of the Edinburgh Mathematical SocietyMore details
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Edition type
Revised edition
Illustrations
163 Tables, unspecified; 28 Line drawings, unspecified
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 32 mm
Weight
905 gr
ISBN-13
978-0-521-81205-4 (9780521812054)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Gordon James | Martin Liebeck
Representations and Characters of Groups
Book
01/2005
2nd Edition
Cambridge University Press
Unfortunately, price unknown
No shipping information available
Gordon James | Martin Liebeck
Representations and Characters of Groups
E-Book
01/2005
2nd Edition
Cambridge University Press
€61.99
Available for download
Gordon James
Representations and Characters of Groups
E-Book
10/2001
Cambridge University Press
€51.49
Available for download
Previous edition
Gordon Douglas James | Martin W. Liebeck
Representations and Characters of Groups
Book
07/1993
Cambridge University Press
€68.09
Article exhausted; check for reprint
Persons
Content
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.