Algebras Of Functions On Quantum Groups Part I

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Algebras Of Functions On Quantum Groups Part I

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Author : Leonid I. Korogodski
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Algebras Of Functions On Quantum Groups Part I written by Leonid I. Korogodski 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.

The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.

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.

Introduction To Quantum Groups

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Author : George Lusztig
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-27

Introduction To Quantum Groups written by George Lusztig 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 2010-10-27 with Mathematics categories.

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Affine Lie Algebras And Quantum Groups

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Author : Jürgen Fuchs
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-09

Affine Lie Algebras And Quantum Groups written by Jürgen Fuchs 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 1995-03-09 with Mathematics categories.

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Quantum Group Symmetry And Q Tensor Algebras

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Author : L. C. Biedenharn
language : en
Publisher: World Scientific
Release Date : 1995

Quantum Group Symmetry And Q Tensor Algebras written by L. C. Biedenharn 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 with Science categories.

Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.

Advances In Algebra And Combinatorics

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Author : K. P. Shum
language : en
Publisher: World Scientific
Release Date : 2008

Advances In Algebra And Combinatorics written by K. P. Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics

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Author : Kar Ping Shum
language : en
Publisher: World Scientific
Release Date : 2008-06-17

Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics written by Kar Ping Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-17 with Mathematics categories.

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Lie Groups Geometry And Representation Theory

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Author : Victor G. Kac
language : en
Publisher: Springer
Release Date : 2018-12-12

Lie Groups Geometry And Representation Theory written by Victor G. Kac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)

Noncommutative Geometry And Representation Theory In Mathematical Physics

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Author : Jürgen Fuchs
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Noncommutative Geometry And Representation Theory In Mathematical Physics written by Jürgen Fuchs 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 2005 with Mathematics categories.

Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influentialin physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities. This volume contains the plenary talks fromthe international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitablefor graduate students and researchers interested in mathematical physics.