Representations Of Algebras And Related Topics

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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.

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Genre : Algebra
Author : Andrzej Skowroński
Publisher : European Mathematical Society
Release : 2011
File : 744 Pages
ISBN-13 : 3037191015


Representations Of Algebras And Related Topics

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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

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Genre : Mathematics
Author : Ragnar-Olaf Buchweitz
Publisher : American Mathematical Soc.
Release : 2005
File : 418 Pages
ISBN-13 : 9780821834152


Representation Theory Of Algebras And Related Topics

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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.

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Genre : Computers
Author : Raymundo Bautista
Publisher : American Mathematical Soc.
Release : 1996
File : 428 Pages
ISBN-13 : 0821803964


Trends In Representation Theory Of Algebras And Related Topics

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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.

Product Details :

Genre : Representations of algebras
Author : Andrzej Skowroński
Publisher : European Mathematical Society
Release : 2008
File : 732 Pages
ISBN-13 : 3037190620


Trends In Representation Theory Of Algebras And Related Topics

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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.

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Genre : Mathematics
Author : José Antonio de la Peña
Publisher : American Mathematical Soc.
Release : 2006
File : 282 Pages
ISBN-13 : 9780821838181


Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry

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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.

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Genre : Mathematics
Author : Vlastimil Dlab
Publisher : American Mathematical Soc.
Release : 2004
File : 502 Pages
ISBN-13 : 9780821834169


Lie Algebras And Related Topics

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As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.

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Genre : Mathematics
Author : Daniel J. Britten
Publisher : American Mathematical Soc.
Release : 1986
File : 398 Pages
ISBN-13 : 0821860097


Recent Developments In Quantum Affine Algebras And Related Topics

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This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

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Genre : Mathematics
Author : Naihuan Jing
Publisher : American Mathematical Soc.
Release : 1999
File : 482 Pages
ISBN-13 : 9780821811993


Lie Algebras Lie Superalgebras Vertex Algebras And Related Topics

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This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

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Genre : Mathematics
Author : Kailash C. Misra
Publisher : American Mathematical Soc.
Release : 2016-06-28
File : 370 Pages
ISBN-13 : 9781470418441


Finite Dimensional Algebras And Related Topics

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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.

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Genre : Mathematics
Author : V. Dlab
Publisher : Springer Science & Business Media
Release : 2013-04-18
File : 392 Pages
ISBN-13 : 9789401715560