Representation Theory of Artin Algebras

This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field.

Maurice Auslander (Author), Idun Reiten (Author), Sverre O. Smalo (Author)

9780521599238, Cambridge University Press

Paperback, published 21 August 1997

440 pages, 6 b/w illus.
22.8 x 15.2 x 2.3 cm, 0.6 kg

'... written in a clear comprehensive style with full proofs. It can very well serve as an excellent reference as well as a textbook for graduate students.' EMS Newletter

This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is a suitable introduction for any mathematician (especially graduate students) to this field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However, other foundational aspects of the subject are developed. These results give concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems, and numerous exercises.

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.

Subject Areas: Algebra [PBF]