Elements of the Representation Theory of Associative Algebras

Daniel Simson; Andrzej Skowronski

doi:10.1017/CBO9780511619403

The final part of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. This volume provides an introduction to the representation theory of representation-infinite tilted algebras from the point of view of the time-wild dichotomy. Also included is a collection of selected results relating to the material discussed in all three volumes. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but will also be of interest to mathematicians in other fields. Proofs are presented in complete detail, and the text includes many illustrative examples and a large number of exercises at the end of each chapter, making the book suitable for courses, seminars, and self-study.

'… indispensable both for researchers and for graduate students interested in modern representation theory.'

Source: European Mathematical Society Newsletter

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Elements of the Representation Theory of Associative Algebras

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Introduction
pp ix-xii

XV - Tubular extensions and tubular coextensions of algebras
pp 1-64

XVI - Branch algebras
pp 65-102

XVII - Tilted algebras of Euclidean type
pp 103-212

XVIII - Wild hereditary algebras and tilted algebras of wild type
pp 213-308

XIX - Tame and wild representation type of algebras
pp 309-358

XX - Perspectives
pp 359-404

Bibliography
pp 405-450

Index
pp 451-454

List of symbols
pp 455-456

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