Elements of the Representation Theory of Associative Algebras
Elements of the Representation Theory of Associative Algebras
The second of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers, geometry of tubes of indecomposable modules, and homological algebra. This volume provides an up-to-date introduction to the representation theory of the representation-infinite hereditary algebras of Euclidean type, as well as to concealed algebras of Euclidean type. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study.
- Self contained, only knowledge from volume one is required for volume two
- Introduces the reader to representation theory by applying tilting theory
- Class tested in courses given by the authors
Reviews & endorsements
"The book is lucid and well written, and the exposition of the material is highly concrete and coherent. The proofs are carefully presented with sufficient enough details. The advanced material exposed in the book is supplied by many well=chosen worked examples and exercises illustrating the main parts of the theory. The book will be very useful on the one hand to graduate students who want to learn advanced topics in the field and on the other hand to researchers and experts as a complete reference guide to central results (many of them not previously found in book form in the representation theory of finite-dimensional algebras as developed in the last 30 years."
Apostolos D. Beligiannis, Mathematical Reviews
Product details
September 2007Paperback
9780521544207
320 pages
227 × 152 × 16 mm
0.456kg
52 exercises
Available
Table of Contents
- Introduction
- 10. Tubes
- 11. Module categories over concealed algebras of Euclidean type
- 12. Regular modules and tubes over concealed algebras of Euclidean type
- 13. Indecomposable modules and tubes over hereditary algebras of Euclidean type
- 14. Minimal representation-infinite algebras
- Bibliography
- Index
- List of symbols.
