This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulate categories.

This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras.

"Algebras, Quivers and Representations" is targeted at researchers and graduate students in algebra, representation theory and triangulate categories. "

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.