Representation Theory of Artin Algebras / Edition 1

by Maurice Auslander, Idun Reiten, Sverre O. Smalo

Overview

This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra. Written by three distinguished mathematicians, it illustrates how the theory of almost split sequences is utilized within representation theory. The authors develop several foundational aspects of the subject. For example, the representations of quivers with relations and their interpretation as modules over the factors of path algebras is discussed in detail. Thorough discussions yield concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems and numerous exercises. It is an invaluable resource for graduate students and researchers.

Product Details

ISBN-13:	9780521599238
Publisher:	Cambridge University Press
Publication date:	08/21/1997
Series:	Cambridge Studies in Advanced Mathematics , #36
Edition description:	New Edition
Pages:	440
Product dimensions:	5.98(w) x 8.98(h) x 0.91(d)

Table of Contents

1. Artin rings; 2. Artin algebras; 3. Examples of algebras and modules; 4. The transpose and the dual; 5. Almost split sequences; 6. Finite representation type; 7. The Auslander-Reiten-quiver; 8. Hereditary algebras; 9. Short chains and cycles; 10. Stable equivalence; 11. Modules determining morphisms.

Editorial Reviews

"Here is the book you may have been waiting for for a long time, maybe for fifteen years: a general introduction to the new representation theory of finite-dimensional algebras....One has to be grateful to the authors for a competent and readable introduction to the subject....The book can be recommended without reservation! It surely will serve as a standard reference." Claus Michael Ringel, Bulletin of the American Mathematical Society

From the Publisher