Representations of Finite Groups - 1st Edition - ISBN: 9780125136600, 9781483269931

Representations of Finite Groups

1st Edition

Authors: Hirosi Nagao Yukio Tsushima
eBook ISBN: 9781483269931
Imprint: Academic Press
Published Date: 28th May 1989
Page Count: 442
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Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups.

Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theoretic versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them.

This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.

Table of Contents

Preface to the English Edition



Chapter 1 Rings and Modules

1. Definitions and Notations

2. Noetherian and Artinian Modules

3. The Radical of a Ring

4. Idempotents

5. Endomorphism Rings

6. The Krull-Schmidt-Azumaya Theorem

7. Completely Reducible Modules

8. Artinian Rings

9. Horn and ⨂

10. Projective and Injective Modules

11. Change of Rings

12. Existence of Injective Hulls

13. Discrete Valuation Rings

14. Algebras over Complete Discrete Valuation Rings


Chapter 2 Algebras and Their Representations

1. Fundamental Concepts of the Representations

2. Algebras over Fields

3. Absolutely Irreducible Representations

4. Simple Algebras

5. Separable Algebras

6. The Schur Index

7. Crossed Products

8. Frobenius Algebras and Symmetric Algebras


Chapter 3 Representations of Groups

1. Representations of Groups and Group Rings

2. Ordinary Representations

3. The Clifford Theory

4. Some Brauer Theorems

5. Projective Representations

6. Introduction to Modular Representation Theory


Chapter 4 Indecomposable Modules

1. Trace Maps

2. H-Projective Modules

3. Vertices and Sources

4. The Green Correspondence

5. Green Correspondences and Endomorphism Rings

6. Endomorphism Rings of Induced Modules

7. The Green Indecomposability Theorem and Its Applications

8. Scott Modules


Chapter 5 Theory of Blocks

1. Defe


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© Academic Press 1987
Academic Press
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About the Author

Hirosi Nagao

Yukio Tsushima

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