Representation Theory of Artin Algebras (Cambridge Studies in Advanced Mathematics, Series Number 36)

This Book Is An Introduction To The Contemporary Representation Theory Of Artin Algebras, By Three Very Distinguished Practitioners In The Field. Beyond Assuming Some First-year Graduate Algebra And Basic Homological Algebra, The Presentation Is Entirely Self-contained, So The Book Is A Suitable Introduction For Any Mathematician (especially Graduate Students) To This 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. However, Other Foundational Aspects Of The Subject Are Developed. 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. Maurice Auslander, Idun Reiten, Sverre O. Smalø. Includes Bibliographical References.

This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra. Written by three distinguished mathematicians, it illustrates how the theory of almost split sequences is utilized within representation theory. The authors develop several foundational aspects of the subject. For example, the representations of quivers with relations and their interpretation as modules over the factors of path algebras is discussed in detail. Thorough discussions yield concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems and numerous exercises. It is an invaluable resource for graduate students and researchers.

https://doi.org/10.1017/CBO9780511623608 Title 1 Contents 7 Introduction 11 I. Artin rings 15 II. Artin algebras 40 III. Examples of algebras and modules 63 IV. The transpose and the dual 114 V. Almost split sequences 150 VI. Finite representation type 205 VII. The Auslander-Reiten-quiver 238 VIII. Hereditary algebras 271 IX. Short chains and cycles 327 X. Stable equivalence 349 XI. Modules determining morphisms 379 Notation 420 Conjectures 423 Open problems 425 Bibliography 427 Relevant conference proceedings 435 Index 437