Local Representation Theory(ISBN=9780521449267) 下载 mobi 免费 pdf 百度网盘 epub 2025 在线 电子书

The aim of this text is to present some of the key results in

the representation theory of finite groups. In order to keep the

account reasonably elementary, so that it can be used for

graduate-level courses, Professor Alperin has concentrated on local

representation theory, emphasising module theory throughout. In

this way many deep results can be obtained rather quickly. After

two introductory chapters, the basic results of Green are proved,

which in turn lead in due course to Brauer's First Main Theorem. A

proof of the module form of Brauer's Second Main Theorem is then

presented, followed by a discussion of Feit's work connecting maps

and the Green correspondence. The work concludes with a treatment,

new in part, of the Brauer-Dade theory. As a text, this book

contains ample material for a one semester course. Exercises are

provided at the end of most sections; the results of some are used

later in the text. Representation theory is applied in number

theory, combinatorics and in many areas of algebra. This book will

serve as an excellent introduction to those interested in the

subject itself or its applications.

Preface

Part I. Semi-Simple Modules

Part II. Projective Modules

Part III. Modules and Subgroups

Part IV. Blocks

Part V. Cyclic Blocks

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书籍介绍

Representation theory has applications to number theory, combinatorics and many areas of algebra. The aim of this text is to present some of the key results in the representation theory of finite groups. Professor Alperin concentrates on local representation theory, emphasizing module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. Exercises are provided at the end of most sections; the results of some are used later in the text.