Cohen-Macaulay Representations

Leuschke, Graham J.; Wiegand, Roger

ISBN 10: 0821875817 / ISBN 13: 9780821875810

Published by American Mathematical Society, 2012

About this Item

Seller Inventory # 18946737-n

Bibliographic Details

• Title: Cohen-Macaulay Representations
• Publisher: American Mathematical Society
• Publication Date: 2012
• Language: English
• ISBN 10: 0821875817
• ISBN 13: 9780821875810
• Binding: Hardcover
• Condition: New

About this title

Synopsis

This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.