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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Book Description American Mathematical Society, United States, 2012. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAN9780821875810

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Roger Wiegand, Graham J. Leuschke
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Book Description American Mathematical Society, United States, 2012. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # AAN9780821875810

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Book Description American Mathematical Society. Hardback. Condition: New. New copy - Usually dispatched within 2 working days. Seller Inventory # B9780821875810

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Book Description American Mathematical Society, 2012. HRD. Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Seller Inventory # CE-9780821875810

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Book Description Amer Mathematical Society, 2012. Hardcover. Condition: Brand New. 367 pages. 10.25x7.25x1.00 inches. In Stock. Seller Inventory # __0821875817

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