Synopses & Reviews
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.
Review
"...a beautifully written book. Anyone wishing to learn the fundamental facts of Brauer's theory of blocks cannot do better than to begin his [or her] study with this text." Bulletin of The London Mathematical Society
Synopsis
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. 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.
Synopsis
This text presents some of the key results in the representation theory of finite groups, and contains ample material for a one semester course.
Table of Contents
Preface; Part I. Semi-Simple Modules: Part II. Projective Modules: Part III. Modules and Subgroups: Part IV. Blocks: Part V. Cyclic Blocks.