Trends In The Representation Theory Of Finite Dimensional Algebras
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Trends In The Representation Theory Of Finite Dimensional Algebras
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Author : Edward L. Green
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Trends In The Representation Theory Of Finite Dimensional Algebras written by Edward L. Green and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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 inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory.
Trends In The Representation Theory Of Finite Dimensional Algebras
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Trends In The Representation Theory Of Finite Dimensional Algebras written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Associative algebras categories.
Trends In Representation Theory Of Algebras And Related Topics
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Author : Andrzej Skowroński
language : en
Publisher: European Mathematical Society
Release Date : 2008
Trends In Representation Theory Of Algebras And Related Topics written by Andrzej Skowroński and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Algebra categories.
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.
Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras
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Author : Dieter Happel
language : en
Publisher:
Release Date : 1988
Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras written by Dieter Happel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Electronic books categories.
This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.
Trends In Representation Theory Of Algebras And Related Topics
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Author : José Antonio de la Peña
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Trends In Representation Theory Of Algebras And Related Topics written by José Antonio de la Peña and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Hopf Algebras Tensor Categories And Related Topics
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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-06
Hopf Algebras Tensor Categories And Related Topics written by Nicolás Andruskiewitsch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-06 with Education categories.
The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.
Modern Trends In Algebra And Representation Theory
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Author : David Jordan
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17
Modern Trends In Algebra And Representation Theory written by David Jordan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.
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.
Recent Developments In Quantum Affine Algebras And Related Topics
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Author : Naihuan Jing
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Recent Developments In Quantum Affine Algebras And Related Topics written by Naihuan Jing and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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.
Handbook Of Algebra
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Author : M. Hazewinkel
language : en
Publisher: Elsevier
Release Date : 2006-05-30
Handbook Of Algebra written by M. Hazewinkel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-30 with Mathematics categories.
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source for information- Provides in-depth coverage of new topics in algebra- Includes references to relevant articles, books and lecture notes
Groups Rings Lie And Hopf Algebras
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-03-31
Groups Rings Lie And Hopf Algebras written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-31 with Mathematics categories.
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.