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

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. We introduce here the notations and terminology we use on algebras and modules, and we briefly recall some of the basic facts from module theory.

Provides an elementary but up-to-date introduction to the representation theory of algebras.