Introduction To The Quantum Yang Baxter Equation And Quantum Groups
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Introduction To The Quantum Yang Baxter Equation And Quantum Groups An Algebraic Approach
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Author : L.A. Lambe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Introduction To The Quantum Yang Baxter Equation And Quantum Groups An Algebraic Approach written by L.A. Lambe 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 2013-11-22 with Mathematics categories.
Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups.
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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Author : Pavel Etingof
language : en
Publisher: OUP Oxford
Release Date : 2005-03-24
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems written by Pavel Etingof and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-24 with Mathematics categories.
The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.
An Introduction To The Relation Between Knots And Quantum Groups Through The Yang Baxter Equation
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Author : Garland M. Lasater (III.)
language : en
Publisher:
Release Date : 1991
An Introduction To The Relation Between Knots And Quantum Groups Through The Yang Baxter Equation written by Garland M. Lasater (III.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Quantum Groups And Lie Theory
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Author : Andrew Pressley
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-17
Quantum Groups And Lie Theory written by Andrew Pressley 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 2002-01-17 with Mathematics categories.
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
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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.
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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Author : Pavel I. Etingof
language : en
Publisher:
Release Date : 2023
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems written by Pavel I. Etingof and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Quantum groups categories.
This text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups.
Yang Baxter Equation And Quantum Groups An Algebraic Approach
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Author : Danny Hunt
language : en
Publisher: NY Research Press
Release Date : 2023-09-26
Yang Baxter Equation And Quantum Groups An Algebraic Approach written by Danny Hunt and has been published by NY Research Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-26 with Mathematics categories.
The Yang-Baxter equation refers to a consistency equation which is based on the concept that particles may preserve their momentum while changing their quantum internal states in some scattering situations. It plays a significant role in theoretical physics and has numerous uses in various areas, ranging from condensed matter to string theory. The Yang-Baxter equation is linked to the universal gates from quantum computing and realizes a unification of some non-associative structures. The quantum Yang-Baxter equation led to the development of the theory of quantum groups. The theory was proposed as the language of quantum groups which is the suitable algebraic language for the solutions of quantum Yang-Baxter equation. This book aims to shed light on some of the unexplored aspects of Yang-Baxter equation and quantum groups. It presents researches and studies performed by experts across the globe. This book will serve as a reference to a broad spectrum of readers.
Quantum Group And Quantum Integrable Systems Nankai Lectures On Mathematical Physics
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Author : Mo-lin Ge
language : en
Publisher: World Scientific
Release Date : 1992-05-30
Quantum Group And Quantum Integrable Systems Nankai Lectures On Mathematical Physics written by Mo-lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-30 with categories.
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.
Yang Baxter Equation And Quantum Enveloping Algebras
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Author : Zhongqi Ma
language : en
Publisher: World Scientific
Release Date : 1993
Yang Baxter Equation And Quantum Enveloping Algebras written by Zhongqi Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
This is the first-ever textbook on the Yang-Baxter equation. A key nonlinear equation for solving two important models in many-body statistical theory - the many-body problem in one dimension with repulsive delta-function interaction presented by Professor Baxter in 1972 - it has become one of the main concerns of physicists and mathematicians in the last ten years. A textbook on this subject which also serves as a reference book is vital for an equation which plays important roles in diverse areas of physics and mathematics like the completely integrable statistical models, conformal field theories, topological field theories, the theory of braid groups, the theory of knots and links, etc. This book arose from lectures given by the author in an attempt to reformulate the results of the rapidly developing research and make the material more accessible. It explains the presentation of the Yang-Baxter equation from statistical models, and expound systematically the meaning and methods of solving for this equation. From the viewpoint of theoretical physics it aims to develop an intuitive understanding of the fundamental knowledge of the Hopf algebras, quantization of Lie bialgebras, and the quantum enveloping algebras, and places emphasis on the introduction of the calculation skill in terms of the physical language.
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.