Elliptic Quantum Groups

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Elliptic Quantum Groups

Hitoshi Konno
Elliptic Quantum Groups Book PDF

Author : Hitoshi Konno
Publisher : Springer Nature
Page : 139 pages
File Size : 40,9 Mb
Release : 2020-09-14
Category : Science
ISBN : 9789811573873

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Elliptic Quantum Groups by Hitoshi Konno Pdf

This is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author’s recent study showed that these elliptic weight functions are identified with Okounkov’s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov’s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT’s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book.

Quantum Groups

Benjamin Enriquez
Quantum Groups Book PDF

Author : Benjamin Enriquez
Publisher : European Mathematical Society
Page : 148 pages
File Size : 43,7 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190477

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Quantum Groups by Benjamin Enriquez Pdf

The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.

A Guide to Quantum Groups

Vyjayanthi Chari,Andrew N. Pressley
A Guide to Quantum Groups Book PDF

Author : Vyjayanthi Chari,Andrew N. Pressley
Publisher : Cambridge University Press
Page : 672 pages
File Size : 47,7 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.

Quantum Group Symmetry and Q-tensor Algebras

L. C. Biedenharn,M. A. Lohe
Quantum Group Symmetry and Q tensor Algebras Book PDF

Author : L. C. Biedenharn,M. A. Lohe
Publisher : World Scientific
Page : 305 pages
File Size : 45,5 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.

Introduction to Quantum Groups

Masud Chaichian,Andrei Pavlovich Demichev
Introduction to Quantum Groups Book PDF

Author : Masud Chaichian,Andrei Pavlovich Demichev
Publisher : World Scientific
Page : 362 pages
File Size : 40,9 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.

Introduction to Quantum Groups

George Lusztig
Introduction to Quantum Groups Book PDF

Author : George Lusztig
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 43,6 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.

Discrete Integrable Systems

J.J. Duistermaat
Discrete Integrable Systems Book PDF

Author : J.J. Duistermaat
Publisher : Springer
Page : 0 pages
File Size : 55,6 Mb
Release : 2010-08-15
Category : Mathematics
ISBN : 0387566236

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Discrete Integrable Systems by J.J. Duistermaat Pdf

This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The theory of QRT maps arose from problems in mathematical physics, involving difference equations. The application of QRT maps to these and other problems in the literature, including Poncelet mapping and the elliptic billiard, is examined in detail. The link between elliptic fibrations and completely integrable Hamiltonian systems is also discussed. The book begins with a comprehensive overview of the subject, including QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, action on homology classes, and periodic QRT maps. Later chapters cover these topics and more in detail. While QRT maps will be familiar to specialists in algebraic geometry, the present volume makes the subject accessible to mathematicians and graduate students in a classroom setting or for self-study.

Foundations of Quantum Group Theory

Shahn Majid
Foundations of Quantum Group Theory Book PDF

Author : Shahn Majid
Publisher : Cambridge University Press
Page : 668 pages
File Size : 45,7 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.

Topics in Quantum Groups and Finite-Type Invariants

Boris L. Feigin,V. A. Vasilʹev
Topics in Quantum Groups and Finite Type Invariants Book PDF

Author : Boris L. Feigin,V. A. Vasilʹev
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 52,7 Mb
Release : 1998
Category : Mathematics
ISBN : 0821810847

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Topics in Quantum Groups and Finite-Type Invariants by Boris L. Feigin,V. A. Vasilʹev Pdf

Presents the first collection of articles consisting entirely of work by the faculty and students at the Higher Mathematics College at the Independent University of Moscow. The 11 contributions cover symmetry groups of regular polyhedra over finite fields, vector bundles on an elliptical curve and Skylanin algebras, Tutte decomposition for graphs and symmetric matrices, and invarians and homology of spaces of knots in arbitrary manifolds. The focus of the text is on quantum groups and low-dimensional topology. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics

Mo-lin Ge
Quantum Group And Quantum Integrable Systems Nankai Lectures On Mathematical Physics Book PDF

Author : Mo-lin Ge
Publisher : World Scientific
Page : 242 pages
File Size : 48,7 Mb
Release : 1992-05-30
Category : Electronic
ISBN : 9789814555838

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Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics by Mo-lin Ge Pdf

This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.

Quantum Groups

Petr P. Kulish
Quantum Groups Book PDF

Author : Petr P. Kulish
Publisher : Unknown
Page : 432 pages
File Size : 53,8 Mb
Release : 1992
Category : Mathematics
ISBN : UCSD:31822015075856

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Quantum Groups by Petr P. Kulish Pdf

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky, L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A. Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.-- Publisher description.

Quantum Groups

Pavel Etingof
Quantum Groups Book PDF

Author : Pavel Etingof
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 52,7 Mb
Release : 2007
Category : Geometric quantization
ISBN : 9780821837139

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Quantum Groups by Pavel Etingof Pdf

The papers in this volume are based on the talks given at the conference on quantum groups dedicated to the memory of Joseph Donin, which was held at the Technion Institute, Haifa, Israel in July 2004. A survey of Donin's distinguished mathematical career is included. Several articles, which were directly influenced by the research of Donin and his colleagues, deal with invariant quantization, dynamical $R$-matrices, Poisson homogeneous spaces, and reflection equation algebras. The topics of other articles include Hecke symmetries, orbifolds, set-theoretic solutions to the pentagon equations, representations of quantum current algebras, unipotent crystals, the Springer resolution, the Fourier transform on Hopf algebras, and, as a change of pace, the combinatorics of smoothly knotted surfaces. The articles all contain important new contributions to their respective areas and will be of great interest to graduate students and research mathematicians interested in Hopf algebras, quantum groups, and applications. Information for our distributors: This book is copublished with Bar-Ilan University (Ramat-Gan, Israel).

Lectures on Quantum Groups

Pavel I. Etingof,Olivier Schiffmann
Lectures on Quantum Groups Book PDF

Author : Pavel I. Etingof,Olivier Schiffmann
Publisher : Unknown
Page : 264 pages
File Size : 42,9 Mb
Release : 2002
Category : Mathematical physics
ISBN : CORNELL:31924104787407

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

Based on lectures given at Harvard University in 1997, this book is an introduction to the theory of quantum groups and its development between 1982 and 1997. Topics covered include: relevant quasiclassical objects; bialgebras; Hopf algebras; and lie associators.

Quantum Groups and Lie Theory

Andrew Pressley
Quantum Groups and Lie Theory Book PDF

Author : Andrew Pressley
Publisher : Cambridge University Press
Page : 246 pages
File Size : 42,6 Mb
Release : 2002-01-17
Category : Mathematics
ISBN : 113943702X

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Quantum Groups and Lie Theory by Andrew Pressley Pdf

This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.

Quantum Groups

Christian Kassel
Quantum Groups Book PDF

Author : Christian Kassel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 50,9 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.