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    Representations and Characters of Groups (Paperback) By (author) Gordon James, By (author) Martin Liebeck

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    DescriptionThis 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.


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    Title
    Representations and Characters of Groups
    Authors and contributors
    By (author) Gordon James, By (author) Martin Liebeck
    Physical properties
    Format: Paperback
    Number of pages: 466
    Width: 152 mm
    Height: 228 mm
    Thickness: 28 mm
    Weight: 760 g
    Language
    English
    ISBN
    ISBN 13: 9780521003926
    ISBN 10: 052100392X
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 01
    B&T Modifier: Academic Level: 01
    B&T General Subject: 710
    Warengruppen-Systematik des deutschen Buchhandels: 16200
    Ingram Subject Code: MA
    Libri: I-MA
    B&T Modifier: Text Format: 06
    LC subject heading:
    BISAC V2.8: MAT002000
    B&T Merchandise Category: UP
    BISAC V2.8: MAT014000
    DC21: 512.2
    BIC subject category V2: PBG
    B&T Approval Code: A51353060
    LC subject heading:
    DC22: 512.2, 512/.2
    LC classification: QA176 .J36 2001
    Edition
    2, Revised
    Edition statement
    2nd Revised edition
    Illustrations note
    28 b/w illus. 163 tables
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    05 November 2001
    Publication City/Country
    Cambridge
    Review quote
    '... 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 fur 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 Society
    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.