Representation Theory of Artin Algebras
Representation Theory of Artin Algebras
Idun Reiten, Kunstakademiet i Trondheim, Norway
Sverre O. Smalo, Kunstakademiet i Trondheim, Norway
$135.00
USDThis 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.
- Self-contained presentation
- Complete proofs given
- Emphasis on foundational aspects
Reviews & endorsements
"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
Product details
April 2011Adobe eBook Reader
9780511879678
0 pages
0kg
6 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
