A Course in Finite Group Representation Theory

Peter Webb

• Publisher: Cambridge University Press
• Year: 2016
• ISBN:
  9781316786642
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Table of contents

• Cover
• Half title
• Series
• Title
• Copyright
• Contents
• Preface
• 1 Representations, Maschke's Theorem, and Semisimplicity
• 2 The Structure of Algebras for Which Every Module Is Semisimple
• 3 Characters
• 4 The Construction of Modules and Characters
• 5 More on Induction and Restriction: Theorems of Mackey and Clifford
• 6 Representations of p-Groups in Characteristic p and the Radical
• 7 Projective Modules for Finite-Dimensional Algebras
• 8 Projective Modules for Group Algebras
• 9 Changing the Ground Ring: Splitting Fields and the Decomposition Map
• 10 Brauer Characters
• 11 Indecomposable Modules
• 12 Blocks
• Appendix A: Discrete Valuation Rings
• Appendix B: Character Tables
• Bibliography
• Index