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On Characters of Finite Groups / by Michel Broué.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Author/Creator:
- Broué., Author.
- Series:
- Mathematical Lectures from Peking University, 2197-4209
- Language:
- English
- Subjects (All):
- Group theory.
- Categories (Mathematics).
- Algebra, Homological.
- Group Theory and Generalizations.
- Category Theory, Homological Algebra.
- Local Subjects:
- Group Theory and Generalizations.
- Category Theory, Homological Algebra.
- Physical Description:
- 1 online resource (XVI, 246 p. 9 illus., 5 illus. in color.)
- Edition:
- 1版. 2017.
- Place of Publication:
- Singapore : Springer Singapore : Imprint: Springer, 2017.
- Summary:
- This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).
- Contents:
- Tensor Product.-On Representation.-Characteristic 0 representations.-Playing with the base field
- Induction, restriction
- Brauer's theorem and some applications
- Graded representations and characters
- Drinfeld Double
- Appendix A. Basics on Finite Groups
- Appendix B. Assumed results on Galois theory
- Appendix C. Integral elements
- Appendix D. Noetherian rings and modules
- Appendix E. The language of categories and functors
- Bibliography 211.-Index.
- Notes:
- Includes bibliographical references and index.
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 981-10-6878-X
- OCLC:
- 1018471569
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