Quantum Groups
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A Guide To Quantum Groups
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Author : Vyjayanthi Chari
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-27
A Guide To Quantum Groups written by Vyjayanthi Chari 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 1995-07-27 with Mathematics categories.
Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.
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.
Quantum Groups
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Author : Christian Kassel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Groups written by Christian Kassel 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 Mathematics categories.
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.
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 Function algebras 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.
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.
Introduction To Quantum Groups
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Author : Masud Chaichian
language : en
Publisher: World Scientific
Release Date : 1996
Introduction To Quantum Groups written by Masud Chaichian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.
In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.
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.
Lectures On Quantum Groups
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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On Quantum Groups written by Jens Carsten Jantzen 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 Mathematical physics categories.
The material is very well motivated ... Of the various monographs available on quantum groups, this one ... seems the most suitable for most mathematicians new to the subject ... will also be appreciated by a lot of those with considerably more experience. --Bulletin of the London Mathematical Society Since its origin, the theory of quantum groups has become one of the most fascinating topics of modern mathematics, with numerous applications to several sometimes rather disparate areas, including low-dimensional topology and mathematical physics. This book is one of the first expositions that is specifically directed to students who have no previous knowledge of the subject. The only prerequisite, in addition to standard linear algebra, is some acquaintance with the classical theory of complex semisimple Lie algebras. Starting with the quantum analog of $\mathfrak{sl}_2$, the author carefully leads the reader through all the details necessary for full understanding of the subject, particularly emphasizing similarities and differences with the classical theory. The final chapters of the book describe the Kashiwara-Lusztig theory of so-called crystal (or canonical) bases in representations of complex semisimple Lie algebras. The choice of the topics and the style of exposition make Jantzen's book an excellent textbook for a one-semester course on quantum groups.
Quantum Groups
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Author : Vladimir K. Dobrev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-07-10
Quantum Groups written by Vladimir K. Dobrev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-10 with Science categories.
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies
A Quantum Groups Primer
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Author : Shahn Majid
language : en
Publisher: Cambridge University Press
Release Date : 2002-04-04
A Quantum Groups Primer written by Shahn Majid 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 2002-04-04 with Mathematics categories.
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.