Cohen-Macaulay Representations (Mathematical Surveys and Monographs)

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9780821875810: Cohen-Macaulay Representations (Mathematical Surveys and Monographs)
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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.

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Graham J. Leuschke, Roger Wiegand
Published by American Mathematical Society (2012)
ISBN 10: 0821875817 ISBN 13: 9780821875810
New Hardcover Quantity Available: 1
Murray Media
(North Miami Beach, FL, U.S.A.)

Book Description American Mathematical Society, 2012. Hardcover. Condition: New. Never used!. Seller Inventory # P110821875817

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