Representations Of Lie Algebras Quantum Groups And Related Topics
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Representations Of Lie Algebras Quantum Groups And Related Topics
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Author : Naihuan Jing
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-21
Representations Of Lie Algebras Quantum Groups 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 2018-08-21 with Algebra categories.
This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.
Representations Of Lie Algebras Quantum Groups And Related Topics
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Author : Naihuan Jing
language : en
Publisher:
Release Date : 2018
Representations Of Lie Algebras Quantum Groups And Related Topics written by Naihuan Jing and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Algebra categories.
Quantum Groups And Their Representations
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Author : Anatoli Klimyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Groups And Their Representations written by Anatoli Klimyk 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 2012-12-06 with Science categories.
This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Lie Algebras Lie Superalgebras Vertex Algebras And Related Topics
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Author : Kailash C. Misra
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-28
Lie Algebras Lie Superalgebras Vertex Algebras And Related Topics written by Kailash C. Misra 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 2016-06-28 with Group theory and generalizations categories.
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.
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry
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Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry written by Vlastimil Dlab 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 2004 with Associative algebras categories.
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.
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 Affine algebraic groups 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.
Multidimensional Hypergeometric Functions And Representation Theory Of Lie Algebras And Quantum Groups
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Author : A Varchenko
language : en
Publisher: World Scientific
Release Date : 1995-03-29
Multidimensional Hypergeometric Functions And Representation Theory Of Lie Algebras And Quantum Groups written by A Varchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-29 with Mathematics categories.
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik–Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals. Contents:IntroductionConstruction of Complexes Calculating Homology of the Complement of a ConfigurationConstruction of Homology Complexes for Discriminantal ConfigurationAlgebraic Interpretation of Chain Complexes of a Discriminantal ConfigurationQuasiisomorphism of Two-Sided Hochschild Complexes to Suitable One-Sided Hochschild ComplexesBundle Properties of a Discriminantal ConfigurationR-Matrix for the Two-Sided Hochschild ComplexesMonodromyR-Matrix Operator as the Canonical Element, Quantum DoublesHypergeometric IntegralsKac–Moody Lie Algebras Without Serre's Relations and Their DoublesHypergeometric Integrals of a Discriminantal ConfigurationResonances at InfinityDegenerations of Discriminantal ConfigurationsRemarks on Homology Groups of a Configuration with Coefficients in Local Systems More General than Complex One-Dimensional Readership: Mathematicians, theoretical physicists, and graduate students. keywords:Hypergeometric Function;Hypergeometric Type Function;Hypergeometric Integral;Kac-Moody Algebra;Quantum Group;Representations of a Kac-Moody Algebra;Representations of a Quantum Group;Discriminant Configuration;Monodromy “The book is elegantly structured and sticks closely to the point, and is also fairly down to earth … as well as serving as an excellent specialist monograph, it should also be useful as a first exposure to these topics for anyone who likes to learn a subject through the study of a concrete problem.” Bull. London Math. Soc.
Lie Algebras And Their Representations
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Author : Seok-Jin Kang
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lie Algebras And Their Representations written by Seok-Jin Kang 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 1996 with Lie algebras categories.
Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
Representation Of Lie Groups And Related Topics
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Author : Anatoliĭ Moiseevich Vershik
language : en
Publisher: CRC Press
Release Date : 1990
Representation Of Lie Groups And Related Topics written by Anatoliĭ Moiseevich Vershik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Eight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Lie Algebras Cohomology And New Applications To Quantum Mechanics
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Author : Niky Kamran
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Lie Algebras Cohomology And New Applications To Quantum Mechanics written by Niky Kamran 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 1994 with Mathematics categories.
This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.