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

Cambridge Studies in Advanced Mathematics #30

by D.J. Benson

This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion 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 some detail.

Genres: Mathematics

260 pages, Hardcover

First published January 1, 1991

Reviews

[Andrew · Rating 3 out of 5]

The use of "basic" in the title is tautological. A theory is basic in volume 1 if it is slightly below the author's expectation in volume 2.

The author warns that chapter 4, on Auslander-Reiten theory, is "not entirely painless." For the first half of the chapter I did not believe this, and then the material became very technical.