Cohen Macaulay Representations
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Cohen Macaulay Representations
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Author : Graham J. Leuschke
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-05-02
Cohen Macaulay Representations written by Graham J. Leuschke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-02 with Mathematics categories.
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.
Maximal Cohen Macaulay Modules Over Non Isolated Surface Singularities And Matrix Problems
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Author : Igor Burban
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-13
Maximal Cohen Macaulay Modules Over Non Isolated Surface Singularities And Matrix Problems written by Igor Burban and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-13 with Cohen-Macaulay modules categories.
In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
Maximal Cohen Macaulay Modules Over Cohen Macaulay Rings
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Author : Yūji Yoshino
language : en
Publisher: Cambridge University Press
Release Date : 1990-06-28
Maximal Cohen Macaulay Modules Over Cohen Macaulay Rings written by Yūji Yoshino and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-06-28 with Mathematics categories.
The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.
Representations Of Algebras
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Author : P. Webb
language : en
Publisher: Cambridge University Press
Release Date : 1986-01-08
Representations Of Algebras written by P. Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-08 with Mathematics categories.
The latest developments in representation theory with emphasis on the representation type of finite-dimensional algebras.
Maximal Cohen Macaulay Modules Over Cohen Macaulay Rings
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Author : Y. Yoshino
language : en
Publisher:
Release Date : 1990
Maximal Cohen Macaulay Modules Over Cohen Macaulay Rings written by Y. Yoshino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Cohen-Macaulay modules categories.
The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.
Algebra Representation Theory
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Author : Klaus W. Roggenkamp
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-31
Algebra Representation Theory written by Klaus W. Roggenkamp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-31 with Mathematics categories.
Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.
Maximal Cohen Macaulay Modules And Tate Cohomology
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Author : Ragnar-Olaf Buchweitz
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-16
Maximal Cohen Macaulay Modules And Tate Cohomology written by Ragnar-Olaf Buchweitz and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.
This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.
Trends In Representation Theory Of Algebras And Related Topics
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Author : Andrzej Skowroński
language : en
Publisher: European Mathematical Society
Release Date : 2008
Trends In Representation Theory Of Algebras And Related Topics written by Andrzej Skowroński and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Representations of algebras categories.
This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
Homological Theory Of Representations
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Author : Henning Krause
language : en
Publisher: Cambridge University Press
Release Date : 2021-11-18
Homological Theory Of Representations written by Henning Krause and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Mathematics categories.
This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.
Determinantal Rings
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Author : Winfried Bruns
language : en
Publisher: Springer
Release Date : 2006-11-14
Determinantal Rings written by Winfried Bruns and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.