Representation Theory of Algebras and Related Topics PDF Download

Author: Raymundo Bautista
Publisher: American Mathematical Soc.
ISBN: 9780821803967
Category : Computers
Languages : en
Pages : 428

View

Book Description
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
ISBN: 9783037190623
Category : Representations of algebras
Languages : en
Pages : 732

View

Book Description
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
Publisher: American Mathematical Soc.
ISBN: 0821834150
Category : Mathematics
Languages : en
Pages : 418

View

Book Description
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
Publisher: American Mathematical Soc.
ISBN: 0821834169
Category : Mathematics
Languages : en
Pages : 502

View

Book Description
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: Karin Erdmann
Publisher: Springer
ISBN: 3319919989
Category : Mathematics
Languages : en
Pages : 304

View

Book Description
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: José Antonio de la Peña
Publisher: American Mathematical Soc.
ISBN: 0821838180
Category : Mathematics
Languages : en
Pages : 282

View

Book Description
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
Publisher:
ISBN: 9783037196014
Category : Algebra
Languages : en
Pages : 728

View

Book Description
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: Pavel I. Etingof
Publisher: American Mathematical Soc.
ISBN: 0821853511
Category : Mathematics
Languages : en
Pages : 240

View

Book Description
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.

Author: Martin Lorenz
Publisher: American Mathematical Soc.
ISBN: 1470436809
Category : Categories (Mathematics)
Languages : en
Pages : 654

View

Book Description
Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.

Author: Ibrahim Assem
Publisher: Springer Nature
ISBN: 3030351181
Category : Mathematics
Languages : en
Pages : 318

View

Book Description
This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.