Representation Theory of Artin Algebras

Introducing the contemporary representation theory of Artin algebras, this work assumes some first-year graduate algebra and basic homological algebra. The overall presentation of the text, however, is entirely self-contained, making it accessible for any mathematicians (especially graduate students) wanting an introduction to the 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. Other foundational aspects of the subject are also developed, such as the representations of quivers with relations and their interpretation as modules over the factors of path algebras is discussed in detail. 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.