Homological Theory Of Representations
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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.
Representation Theory
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Author : Alexander Zimmermann
language : en
Publisher: Springer
Release Date : 2014-08-15
Representation Theory written by Alexander Zimmermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Mathematics categories.
Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Rational Representations The Steenrod Algebra And Functor Homology
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Author : Vincent Franjou
language : en
Publisher:
Release Date : 2003
Rational Representations The Steenrod Algebra And Functor Homology written by Vincent Franjou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The book presents aspects of homological algebra in functor categories, with emphasis on polynomial functors between vector spaces over a finite field. With these foundations in place, the book presents applications to representation theory, algebraic topology and $K$-theory. As these applications reveal, functor categories offer powerful computational techniques and theoretical insights. T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander then presents applications to the rational representations of general linear groups. L. Schwartz emphasizes the relation of functor categories to the Steenrod algebra. Finally, V. Franjou and T. Pirashvili present A. Scorichenko's understanding of the stable $K$-theory of rings as functor homology. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.
Representations And Cohomology Volume 1 Basic Representation Theory Of Finite Groups And Associative Algebras
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Author : D. J. Benson
language : en
Publisher: Cambridge University Press
Release Date : 1991-03-21
Representations And Cohomology Volume 1 Basic Representation Theory Of Finite Groups And Associative Algebras written by D. J. Benson 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 1991-03-21 with Mathematics categories.
This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail.
Extended Abstracts Spring 2015
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Author : Dolors Herbera
language : en
Publisher: Birkhäuser
Release Date : 2016-11-30
Extended Abstracts Spring 2015 written by Dolors Herbera and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Mathematics categories.
This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.
Homological Algebra Of Semimodules And Semicontramodules
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Author : Leonid Positselski
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
Homological Algebra Of Semimodules And Semicontramodules written by Leonid Positselski 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 2010-09-02 with Mathematics categories.
This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.
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.
Representations And Cohomology
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Author : David J. Benson
language : en
Publisher:
Release Date : 1991
Representations And Cohomology written by David J. Benson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Homology theory categories.
Elements Of The Representation Theory Of Associative Algebras Volume 2 Tubes And Concealed Algebras Of Euclidean Type
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Author : Daniel Simson
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-06
Elements Of The Representation Theory Of Associative Algebras Volume 2 Tubes And Concealed Algebras Of Euclidean Type written by Daniel Simson 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 2007-09-06 with Mathematics categories.
The second of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers, geometry of tubes of indecomposable modules, and homological algebra. This volume provides an up-to-date introduction to the representation theory of the representation-infinite hereditary algebras of Euclidean type, as well as to concealed algebras of Euclidean type. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study.
Representations Of Algebras
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Author : José-Antonio de la Peña
language : en
Publisher: Springer Nature
Release Date : 2022-10-22
Representations Of Algebras written by José-Antonio de la Peña and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-22 with Mathematics categories.
This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form. The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the Harada–Sai lemma, chain conditions, and Auslander–Reiten theory. Noteworthy and significant results covered in the book include the Brauer–Thrall conjectures, Drozd’s theorem, and criteria to distinguish tame from wild algebras. This text may serve as the basis for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. The originality of the exposition and the wealth of topics covered also make it a valuable resource for more established researchers.