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 : 2012-01-01
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 2012-01-01 with Mathematics categories.
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.
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.
Cohen Macaulay Rings
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Author : Winfried Bruns
language : en
Publisher: Cambridge University Press
Release Date : 1998-06-18
Cohen Macaulay Rings written by Winfried Bruns 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 1998-06-18 with Mathematics categories.
In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.
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.
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.
Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library.
Local Cohomology
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Author : M. P. Brodmann
language : en
Publisher: Cambridge University Press
Release Date : 2013
Local Cohomology written by M. P. Brodmann 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 2013 with Mathematics categories.
On its original publication, this algebraic introduction to Grothendieck's local cohomology theory was the first book devoted solely to the topic and it has since become the standard reference for graduate students. This second edition has been thoroughly revised and updated to incorporate recent developments in the field.
Integral Closure Of Ideals Rings And Modules
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Author : Craig Huneke
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12
Integral Closure Of Ideals Rings And Modules written by Craig Huneke 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 2006-10-12 with Mathematics categories.
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
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 Algebra 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.
Interactions Between Ring Theory And Representations Of Algebras
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Author : Freddy Van Oystaeyen
language : en
Publisher: CRC Press
Release Date : 2000-04-05
Interactions Between Ring Theory And Representations Of Algebras written by Freddy Van Oystaeyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-05 with Mathematics categories.
This work is based on a set of lectures and invited papers presented at a meeting in Murcia, Spain, organized by the European Commission's Training and Mobility of Researchers (TMR) Programme. It contains information on the structure of representation theory of groups and algebras and on general ring theoretic methods related to the theory.