Representation Theory Of Algebras And Related Topics

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 43,9 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 : Raymundo Bautista,Roberto Martínez-Villa,José Antonio de la Peña
Publisher : American Mathematical Soc.
Page : 428 pages
File Size : 55,6 Mb
Release : 1996
Category : Computers
ISBN : 0821803964

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

These proceedings report a number of lecture series delivered during the Workshop on Representation Theory of Algebras and Related Topics held at Universidad Nacional Autonoma de Mexico (UNAM) in August 1994. The workshop was dedicated to recent advances in the field and its interaction with other areas of mathematics, such as algebraic geometry, ring theory, and representation of groups. The program of the Workshop consisted of 9 lecture series. In addition there was a Tame Day consisting of 6 lectures reporting on the recent advances in the study of tame algebras and their module categories. During the Workshop there was a session devoted to the exhibition of computer programs developed by participants. These programs are implementations of algorithms related to the calculation of important aspects of algebras and their module categories.

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Page : 732 pages
File Size : 51,7 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 : Ragnar-Olaf Buchweitz,Helmut Lenzing
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 53,7 Mb
Release : 2005
Category : Representations of algebras
ISBN : 9780821834152

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Representations of Algebras and Related Topics by Ragnar-Olaf Buchweitz,Helmut Lenzing Pdf

Twelve-year-old Molly and her ten-year-old brother, Michael, have never liked their younger stepsister, Heather. Ever since their parents got married, she's made Molly and Michael's life miserable. Now their parents have moved them all to the country to live in a house that used to be a church, with a cemetery in the backyard. If that's not bad enough, Heather starts talking to a ghost named Helen and warning Molly and Michael that Helen is coming for them. Molly feels certain Heather is in some kind of danger, but every time she tries to help, Heather twists things around to get her into trouble. It seems as if things can't get any worse. But they do -- when Helen comes. "Genuinely scary, complete with dark secrets from the past, unsettled graves, and a very real ghost." -- The Bulletin of the Center for Children's Books "An unusually scary, well-crafted ghost fantasy." -- Kirkus Reviews

Author : Vlastimil Dlab,Claus Michael Ringel
Publisher : American Mathematical Soc.
Page : 502 pages
File Size : 40,6 Mb
Release : 2004
Category : Associative algebras
ISBN : 9780821834169

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Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by Vlastimil Dlab,Claus Michael Ringel Pdf

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.

Author : David J. Benson
Publisher : European Mathematical Society
Page : 1 pages
File Size : 41,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9783037191255

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Advances in Representation Theory of Algebras by David J. Benson Pdf

This volume presents a collection of articles devoted to representations of algebras and related topics. Dististinguished experts in this field presented their work at the International Conference on Representations of Algebras, which took place in Bielefeld in 2012. Many of the expository surveys are included here. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject.

Author : José Antonio de la Peña,Raymundo Bautista
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 47,8 Mb
Release : 2006
Category : Representations of algebras
ISBN : 9780821838181

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Trends in Representation Theory of Algebras and Related Topics by José Antonio de la Peña,Raymundo Bautista Pdf

This book is based on lectures given during a Workshop on Representations of Algebras and Related Topics. Some additional articles are included in order to complete a panoramic view of the main trends of the subject. The volume contains original presentations by leading algebraists addressed to specialists as well as to a broader mathematical audience. The articles include new proofs, examples, and detailed arguments. Topics under discussion include moduli spaces associated to quivers, canonical basis of quantum algebras, categorifications and derived categories, $A$-infinity algebras and functor categories, cluster algebras, support varieties for modules and complexes, the Gabriel-Roiter measure for modules, and selfinjective algebras.

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : Unknown
Page : 728 pages
File Size : 49,8 Mb
Release : 2011
Category : Algebra
ISBN : 3037196017

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata 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, combinatorics, quantum algebras, 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 quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, quantum loop algebras, Nakajima quiver varieties, Yang-Baxter equations, T-systems and Y-systems, dilogarithm and quantum dilogarithm identities, stable module categories, localizing and colocalizing subcategories, cohomologies of groups, support varieties, fusion systems, Hochschild cohomologies, weighted projective lines, coherent sheaves, Kleinian and Fuchsian singularities, stable categories of vector bundles, nilpotent operators, Artin-Schelter regular algebras, Fano algebras, deformations of algebras, module varieties, degenerations of modules, singularities of orbit closures, coalgebras and comodules, representation types of algebras and coalgebras, Tits and Euler forms of algebras, Galois coverings of algebras, tilting and cluster tilting theory, algebras of small homological dimensions, Auslander-Reiten theory. The 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. They contain a large number of examples and open problems and give new perspectives for research in the field.

Author : David J. Benson,Henning Krause,Andrzej Skowroński
Publisher : Unknown
Page : 367 pages
File Size : 42,8 Mb
Release : 2014
Category : MATHEMATICS
ISBN : 3037196254

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Advances in Representation Theory of Algebras by David J. Benson,Henning Krause,Andrzej Skowroński Pdf

This volume presents a collection of articles devoted to representations of algebras and related topics. Dististinguished experts in this field presented their work at the International Conference on Representations of Algebras which took place 2012 in Bielefeld. Many of the expository surveys are included here. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject.

Author : Karin Erdmann,Thorsten Holm
Publisher : Springer
Page : 304 pages
File Size : 44,7 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783319919980

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Algebras and Representation Theory by Karin Erdmann,Thorsten Holm Pdf

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

Author : V. Dlab,Leonard Scott
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 42,9 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401715560

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Finite Dimensional Algebras and Related Topics by V. Dlab,Leonard Scott Pdf

Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Author : Vlastimil Dlab,Claus Michael Ringel
Publisher : American Mathematical Soc.
Page : 508 pages
File Size : 52,6 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821871455

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Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by Vlastimil Dlab,Claus Michael Ringel Pdf

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.

Author : Ragnar-Olaf Buchweitz,Helmut Lenzing
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 40,7 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821885928

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Representations of Algebras and Related Topics by Ragnar-Olaf Buchweitz,Helmut Lenzing Pdf

This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.

Author : Irving Reiner,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 51,9 Mb
Release : 1971
Category : Mathematics
ISBN : 9780821814215

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Representation Theory of Finite Groups and Related Topics by Irving Reiner,American Mathematical Society Pdf

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 45,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

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Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.