A Guide To Quantum Groups

Author : Vyjayanthi Chari,Andrew N. Pressley
Publisher : Cambridge University Press
Page : 672 pages
File Size : 55,9 Mb
Release : 1995-07-27
Category : Mathematics
ISBN : 0521558840

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A Guide to Quantum Groups by Vyjayanthi Chari,Andrew N. Pressley Pdf

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.

Author : Vyjayanthi Chari
Publisher : Unknown
Page : 651 pages
File Size : 52,9 Mb
Release : 1995
Category : Mathematical physics
ISBN : OCLC:1149195232

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A Guide to Quantum Groups by Vyjayanthi Chari Pdf

Author : George Lusztig
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 51,8 Mb
Release : 2010-10-27
Category : Mathematics
ISBN : 9780817647179

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Introduction to Quantum Groups by George Lusztig Pdf

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.

Author : Christian Kassel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207832

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Quantum Groups by Christian Kassel Pdf

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.

Author : Ross Street
Publisher : Cambridge University Press
Page : 160 pages
File Size : 51,6 Mb
Release : 2007-01-18
Category : Mathematics
ISBN : 9781139461443

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Quantum Groups by Ross Street Pdf

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.

Author : Shahn Majid
Publisher : Cambridge University Press
Page : 668 pages
File Size : 51,5 Mb
Release : 2000
Category : Group theory
ISBN : 0521648688

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Foundations of Quantum Group Theory by Shahn Majid Pdf

A graduate level text which systematically lays out the foundations of Quantum Groups.

Author : Pavel I. Etingof,Olivier Schiffmann
Publisher : Unknown
Page : 242 pages
File Size : 50,9 Mb
Release : 2010
Category : Mathematical physics
ISBN : 1571462074

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Lectures on Quantum Groups by Pavel I. Etingof,Olivier Schiffmann Pdf

Author : Anatoli Klimyk,Konrad Schmüdgen
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642608964

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Quantum Groups and Their Representations by Anatoli Klimyk,Konrad Schmüdgen Pdf

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.

Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 52,5 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

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Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Author : Robert Curtis
Publisher : Cambridge University Press
Page : 315 pages
File Size : 52,6 Mb
Release : 1998-06-11
Category : Mathematics
ISBN : 9780521575874

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The Atlas of Finite Groups - Ten Years On by Robert Curtis Pdf

Proceedings containing twenty articles by leading experts in group theory and its applications.

Author : Masud Chaichian,Andrei Pavlovich Demichev
Publisher : World Scientific
Page : 362 pages
File Size : 44,6 Mb
Release : 1996
Category : Science
ISBN : 9810226233

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Introduction to Quantum Groups by Masud Chaichian,Andrei Pavlovich Demichev Pdf

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.

Author : L. C. Biedenharn,M. A. Lohe
Publisher : World Scientific
Page : 305 pages
File Size : 49,6 Mb
Release : 1995
Category : Science
ISBN : 9789810223311

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Quantum Group Symmetry and Q-tensor Algebras by L. C. Biedenharn,M. A. Lohe Pdf

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.

Author : M. I. Petrashen,J. L. Trifonov
Publisher : Courier Corporation
Page : 338 pages
File Size : 45,7 Mb
Release : 2013-01-03
Category : Science
ISBN : 9780486172729

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Applications of Group Theory in Quantum Mechanics by M. I. Petrashen,J. L. Trifonov Pdf

Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 43,8 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Pdf

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 53,7 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121

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Quantum Theory, Groups and Representations by Peter Woit Pdf

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.