Trends In Representation Theory Of Algebras And Related Topics

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Page : 732 pages
File Size : 46,8 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 : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 45,5 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 : José Antonio de la Peña,Raymundo Bautista
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 41,6 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 : 51,7 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 : Vlastimil Dlab,Claus Michael Ringel
Publisher : American Mathematical Soc.
Page : 502 pages
File Size : 50,6 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 : Ragnar-Olaf Buchweitz,Helmut Lenzing
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 42,8 Mb
Release : 2024-06-01
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 : 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 : David J. Benson,Henning Krause,Andrzej Skowroński
Publisher : Unknown
Page : 367 pages
File Size : 47,8 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 : David Jordan,Nadia Mazza,Sibylle Schroll
Publisher : Cambridge University Press
Page : 407 pages
File Size : 55,6 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009097352

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Modern Trends in Algebra and Representation Theory by David Jordan,Nadia Mazza,Sibylle Schroll Pdf

Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Author : Edward L. Green,Birge Huisgen-Zimmermann
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 49,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821809280

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Trends in the Representation Theory of Finite Dimensional Algebras by Edward L. Green,Birge Huisgen-Zimmermann Pdf

This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce the beginning researcher to cutting-edge topics in representation theory. The book will also provide inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory. It's features include: work outlining significant progress on long-standing open problems; survey articles offering both overviews and introductions to various subfields of the topic; and, expositions reflecting the interplay between the representation theory of algebras and other fields.

Author : Aslak Bakke Buan,Henning Krause,Øyvind Solberg
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 2023
Category : Electronic
ISBN : 3985470545

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Representations of Algebras and Related Structures by Aslak Bakke Buan,Henning Krause,Øyvind Solberg Pdf

Author : Ibrahim Assem,Christof Geiß,Sonia Trepode
Publisher : American Mathematical Soc.
Page : 257 pages
File Size : 43,6 Mb
Release : 2021-01-06
Category : Education
ISBN : 9781470451592

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Advances in Representation Theory of Algebras by Ibrahim Assem,Christof Geiß,Sonia Trepode Pdf

The Seventh ARTA (“Advances in Representation Theory of Algebras VII”) conference took place at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México, in Mexico City, from September 24–28, 2018, in honor of José Antonio de la Peña's 60th birthday. Papers in this volume cover topics Professor de la Peña worked on, such as covering theory, tame algebras, and the use of quadratic forms in representation theory. Also included are papers on the categorical approach to representations of algebras and relations to Lie theory, Cohen–Macaulay modules, quantum groups and other algebraic structures.

Author : Raymundo Bautista,Roberto Martínez-Villa,José Antonio de la Peña
Publisher : American Mathematical Soc.
Page : 428 pages
File Size : 49,6 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 : Michael Barot
Publisher : Springer
Page : 179 pages
File Size : 52,7 Mb
Release : 2014-12-29
Category : Mathematics
ISBN : 9783319114750

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Introduction to the Representation Theory of Algebras by Michael Barot Pdf

This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations, explaining the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.

Author : Henning Krause,Peter Littelmann,Gunter Malle,Karl-Hermann Neeb,Christoph Schweigert
Publisher : Unknown
Page : 0 pages
File Size : 50,9 Mb
Release : 2017
Category : Affine algebraic groups
ISBN : 3037191716

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Representation Theory -- Current Trends and Perspectives by Henning Krause,Peter Littelmann,Gunter Malle,Karl-Hermann Neeb,Christoph Schweigert Pdf

From April 2009 until March 2016, the German Science Foundation generously supported the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, which are also reflected in the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles. This volume covers current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras, and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject.