Cohen-Macaulay Representations (eBook)

Graham J Leuschke (Autor)

eBook Download: PDF

2012
367 Seiten
American Mathematical Society (Verlag)
978-0-8218-8790-5 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 5.2.2012
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 0-8218-8790-4 / 0821887904
• ISBN-13: 978-0-8218-8790-5 / 9780821887905