Linear Representations Of Partially Ordered Sets And Vector Space Categories

Author : Daniel Simson
Publisher : CRC Press
Page : 516 pages
File Size : 46,5 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 2881248284

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Linear Representations of Partially Ordered Sets and Vector Space Categories by Daniel Simson Pdf

This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.

Author : José Antonio de la Pe?a,Ernesto Vallejo,Natig M. Atakishiyev
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 55,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821836309

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Algebraic Structures and Their Representations by José Antonio de la Pe?a,Ernesto Vallejo,Natig M. Atakishiyev Pdf

The Latin-American conference on algebra, the XV Coloquio Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of plenary sessions of general interest and special sessions on algebraic combinatorics, associative rings, cohomology of rings and algebras, commutative algebra, group representations, Hopf algebras, number theory, quantum groups, and representation theory of algebras. This proceedings volume contains original research papers related to talks at the colloquium. In addition, there are several surveys presenting important topics to a broad mathematical audience. There are also two invited papers by Raymundo Bautista and Roberto Martinez, founders of the Mexican school of representation theory of algebras. The book is suitable for graduate students and researchers interested in algebra.

Author : P. Dräxler,G. Michler,C.M. Ringel
Publisher : Birkhäuser
Page : 358 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887168

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Computational Methods for Representations of Groups and Algebras by P. Dräxler,G. Michler,C.M. Ringel Pdf

This book presents material from 3 survey lectures and 14 additional invited lectures given at the Euroconference "Computational Methods for Representations of Groups and Algebras" held at Essen University in April 1997. The purpose of this meeting was to provide a survey of general theoretical and computational methods and recent advances in the representation theory of groups and algebras. The foundations of these research areas were laid in survey articles by P. Dräxler and R. Nörenberg on "Classification problems in the representation theory of finite-dimensional algebras", R. A. Wilson on "Construction of finite matrix groups" and E. Green on "Noncommutative Gröbner bases, and projective resolutions". Furthermore, new applications of the computational methods in linear algebra to the revision of the classification of finite simple sporadic groups are presented. Computational tools (including high-performance computations on supercomputers) have become increasingly important for classification problems. They are also inevitable for the construction of projective resolutions of finitely generated modules over finite-dimensional algebras and the study of group cohomology and rings of invariants. A major part of this book is devoted to a survey of algorithms for computing special examples in the study of Grothendieck groups, quadratic forms and derived categories of finite-dimensional algebras. Open questions on Lie algebras, Bruhat orders, Coxeter groups and Kazhdan Lusztig polynomials are investigated with the aid of computer programs. The contents of this book provide an overview on the present state of the art. Therefore it will be very useful for graduate students and researchers in mathematics, computer science and physics.

Author : Claus M. Ringel
Publisher : Springer
Page : 390 pages
File Size : 41,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391272

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Tame Algebras and Integral Quadratic Forms by Claus M. Ringel Pdf

Author : David Arnold
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 54,6 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9781441987501

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Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold Pdf

The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 43,8 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 285 pages
File Size : 45,6 Mb
Release : 2017-04-11
Category : Mathematics
ISBN : 9781351869867

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Algebras, Rings and Modules, Volume 2 by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Author : Raymundo Bautista,Roberto Martínez-Villa,José Antonio de la Peña
Publisher : American Mathematical Soc.
Page : 780 pages
File Size : 48,8 Mb
Release : 1996
Category : Mathematics
ISBN : 0821803956

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Representation Theory of Algebras by Raymundo Bautista,Roberto Martínez-Villa,José Antonio de la Peña Pdf

The ICRA VII was held at Cocoyoc, Mexico, in August 1994. This was the second time that the ICRA was held in Mexico: ICRA III took place in Puebla in 1980. The 1994 conference included 62 lectures, all listed in these Proceedings. Not all contributions presented, however, appear in this book. Most papers in this volume are in final form with complete proofs, with the only exception being the paper of Leszczynski and Skowronski, Auslander algebras of tame representation type, that the editors thought useful to include.

Author : Ibrahim Assem,Andrzej Skowronski,Daniel Simson
Publisher : Cambridge University Press
Page : 34 pages
File Size : 40,6 Mb
Release : 2006-02-13
Category : Mathematics
ISBN : 9781139443180

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Elements of the Representation Theory of Associative Algebras: Volume 1 by Ibrahim Assem,Andrzej Skowronski,Daniel Simson Pdf

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.

Author : Dikran Dikranjan,Luigi Salce
Publisher : CRC Press
Page : 381 pages
File Size : 54,8 Mb
Release : 2019-05-31
Category : Mathematics
ISBN : 9780429530067

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Abelian Groups, Module Theory, and Topology by Dikran Dikranjan,Luigi Salce Pdf

Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Page : 732 pages
File Size : 45,5 Mb
Release : 2008
Category : Representations of algebras
ISBN : 3037190620

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Trends in Representation Theory of Algebras and Related Topics by Andrzej Skowroński Pdf

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.

Author : Alberto Facchini,Evan Houston,Luigi Salce
Publisher : CRC Press
Page : 530 pages
File Size : 55,8 Mb
Release : 2020-02-10
Category : Mathematics
ISBN : 0824750810

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Rings, Modules, Algebras, and Abelian Groups by Alberto Facchini,Evan Houston,Luigi Salce Pdf

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological

Author : Maurice Auslander,Idun Reiten,Sverre O. Smalo
Publisher : Cambridge University Press
Page : 444 pages
File Size : 41,9 Mb
Release : 1997-08-21
Category : Mathematics
ISBN : 0521599237

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Representation Theory of Artin Algebras by Maurice Auslander,Idun Reiten,Sverre O. Smalo Pdf

This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is suitable for any mathematicians (especially graduate students) wanting an introduction to this active field.'...written in a clear comprehensive style with full proofs. It can very well serve as an excellent reference as well as a textbook for graduate students.' EMS Newletter

Author : K.M. Rangaswamy,David Arnold
Publisher : CRC Press
Page : 434 pages
File Size : 43,9 Mb
Release : 1996-08-16
Category : Mathematics
ISBN : 0824797892

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Abelian Groups and Modules by K.M. Rangaswamy,David Arnold Pdf

Contains the proceedings of an international conference on abelian groups and modules held recently in Colorado Springs. Presents the latest developments in abelian groups that have facilitated cross-fertilization of new techniques from diverse areas such as the representation theory of posets, model theory, set theory, and module theory.

Author : Alexandra I. Kostrikin
Publisher : CRC Press
Page : 480 pages
File Size : 40,7 Mb
Release : 1996-02-09
Category : Mathematics
ISBN : 2884490302

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Exercises in Algebra by Alexandra I. Kostrikin Pdf

This book is a collection of exercises for courses in higher algebra, linear algebra and geometry. It is helpful for postgraduate students in checking the solutions and answers to the exercises.