Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups (Cambridge Studies in Advanced Mathematics, Series Number 11) - Hardcover

Alperin, J. L.

Hardcover

ISBN 10: 0521306604 ISBN 13: 9780521306607

Publisher: Cambridge University Press, 1986

Synopsis

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.

About this title

Book Description

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 by concentrating on local representation theory, and emphasizing module theory throughout.

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

Edition details

• Publisher: Cambridge University Press
• Publication date: 1986
• Language: English
• ISBN 10: 0521306604
• ISBN 13: 9780521306607
• Binding: Hardcover
• Number of pages: 192