Author: L.A. Lambe Publisher: Springer Science & Business Media ISBN: 1461541093 Category : Mathematics Languages : en Pages : 314
Book Description
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.
Author: Danny Hunt Publisher: NY Research Press ISBN: 9781647254414 Category : Mathematics Languages : en Pages : 0
Book Description
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.
Author: Andrew Pressley Publisher: Cambridge University Press ISBN: 9781139437028 Category : Mathematics Languages : en Pages : 246
Book Description
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.
Author: Christian Kassel Publisher: Springer Science & Business Media ISBN: 1461207835 Category : Mathematics Languages : en Pages : 540
Book Description
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: Vladimir K. Dobrev Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110427788 Category : Science Languages : en Pages : 450
Book Description
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
Author: Mo-lin Ge Publisher: World Scientific ISBN: 9814555835 Category : Languages : en Pages : 242
Book Description
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.
Author: Zhong-qi Ma Publisher: World Scientific ISBN: 9814504262 Category : Science Languages : en Pages : 331
Book Description
The exact solution of C N Yang's one-dimensional many-body problem with repulsive delta-function interactions and R J Baxter's eight-vertex statistical model are brilliant achievements in many-body statistical physics. A nonlinear equation, now known as the Yang-Baxter equation, is the key to the solution of both problems. The Yang-Baxter equation has also come to play an important role in such diverse topics as completely integrable statistical models, conformal and topological field theories, knots and links, braid groups and quantum enveloping algebras.This pioneering textbook attempts to make accessible results in this rapidly-growing area of research. The author presents the mathematical fundamentals at the outset, then develops an intuitive understanding of Hopf algebras, quantisation of Lie bialgebras and quantum enveloping algebras. The historical derivation of the Yang-Baxter equation from statistical models is recounted, and the interpretation and solution of the equation are systematically discussed. Throughout, emphasis is placed on acquiring calculation skills through physical understanding rather than achieving mathematical rigour.Originating from the author's own research experience and lectures, this book will prove both an excellent graduate text and a useful work of reference.
Author: Florin Felix Nichita Publisher: MDPI ISBN: 3038973246 Category : Mathematics Languages : en Pages : 239
Book Description
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms
Author: L.A. Lambe
Author: Danny Hunt
Author: Andrew Pressley
Author: Christian Kassel
Author: Vladimir K. Dobrev
Author: Mo-lin Ge
Author: Zhong-qi Ma
Author: Florin Felix Nichita
Author: Shahn Majid
Author: Masud Chaichian