Overview
- Reveals the beauty of character theory of finite groups
- Familiarizes readers with the language of categories
- Offers readers broader coverage than books that focus almost exclusively on groups
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Lectures from Peking University (MLPKU)
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Table of contents (8 chapters)
Keywords
About this book
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).
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Authors and Affiliations
About the author
He is a Foreign Honorary Member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, a Senior Member of the Institut Universitaire de France, and a frequent visitor to many institutions in the world.
He is the Editor-in-chief of the Journal of Algebra, and a member of several editorial boards. His main research area is Algebra and Representation Theory, in particular of finite and algebraic groups.
Bibliographic Information
Book Title: On Characters of Finite Groups
Authors: Michel Broué
Series Title: Mathematical Lectures from Peking University
DOI: https://doi.org/10.1007/978-981-10-6878-2
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2017
Hardcover ISBN: 978-981-10-6877-5Published: 29 January 2018
Softcover ISBN: 978-981-13-4964-5Published: 11 December 2018
eBook ISBN: 978-981-10-6878-2Published: 29 December 2017
Series ISSN: 2197-4209
Series E-ISSN: 2197-4217
Edition Number: 1
Number of Pages: XVI, 246
Number of Illustrations: 4 b/w illustrations, 5 illustrations in colour
Topics: Group Theory and Generalizations, Category Theory, Homological Algebra