Cohen-Macaulay Representations - Couverture rigide

Leuschke, Graham J.; Wiegand, Roger

Couverture rigide

ISBN 10 : 0821875817 ISBN 13 : 9780821875810

Editeur : American Mathematical Society, 2012

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 0821875817
• ISBN 13: 9780821875810
• Reliure: Relié
• Nombre de pages: 367
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible