Elements of the Representation Theory of Associative Algebras: Volume 1

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

The aim of this book is to provide an elementary but up-to-date introduction to the representation theory of algebras. Representation-finite and representation-infinite cases are both covered in detail with many concrete examples to illustrate the theory. The treatment is accessible to beginning graduate students and researchers in related areas.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.