Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory

Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory

by Ibrahim Assem, Andrzej Skowronski, Daniel Simson
     
 

ISBN-10: 052158423X

ISBN-13: 9780521584234

Pub. Date: 12/31/2005

Publisher: Cambridge University Press

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary,…  See more details below

Overview

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.

Product Details

ISBN-13:
9780521584234
Publisher:
Cambridge University Press
Publication date:
12/31/2005
Series:
London Mathematical Society Student Texts Series, #65
Pages:
472
Product dimensions:
5.98(w) x 8.98(h) x 1.18(d)

Table of Contents

Introduction; 1. Algebras and modules; 2. Quivers and algebras; 3. Representations and modules; 4. Auslander-Reiten theory; 5. Nakayama algebras and representation-finite group algebras; 6. Tilting theory; 7. Representation-finite hereditary algebras; 8. Tilted algebras; 9. Directing modules and postprojective components; Appendix: categories, functors and homology.

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