Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras

An introduction to modern developments in the representation theory of finite groups and associative algebras.

D. J. Benson (Author)

9780521361347, Cambridge University Press

Hardback, published 21 March 1991

260 pages
23.6 x 15.8 x 1.8 cm, 0.452 kg

"...a very welcome addition to the existing classical literature on representation theory and cohomology of finite groups....fascinating reading for someone who already has a basic knowledge of representation theory and cohomology ...I can recommend this book highly to anyone who works with representation theory and cohomology of finite groups." K. W. Roggenkamp, Mathematical Reviews

This is the first of two volumes which will provide an introduction to modern developments in the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of representations of finite dimensional algebras; the author emphasises modular representations and the homological algebra associated with their categories. This volume is self-contained and independent of its successor, being primarily concerned with the exposition of the necessary background material. The heart of the book is a lengthy introduction to the (Auslander–Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in detail. Much of the material presented here has never appeared in book form. Consequently students and research workers studying group theory and indeed algebra in general will be grateful to Dr Benson for supplying an exposition of a good deal of the essential results of modern representation theory.

1. Background material from rings and modules
2. Homological algebra
3. Modules for group algebra
4. Methods from the representation of algebra
5. Representation rings and Burnside rings
6. Block theory.

Subject Areas: Algebra [PBF]