Introduction To The Quantum Yang Baxter Equation And Quantum Groups An Algebraic Approach
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| Author | : L.A. Lambe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 314 |
| Release | : 2013-11-22 |
| Genre | : Mathematics |
| ISBN | : 1461541093 |
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 | : Christian Kassel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 540 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207835 |
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 | : Florin Felix Nichita |
| Publisher | : MDPI |
| Total Pages | : 239 |
| Release | : 2019-01-31 |
| Genre | : Mathematics |
| ISBN | : 3038973246 |
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms
| Author | : Alexei Borodin |
| Publisher | : Cambridge University Press |
| Total Pages | : 169 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1107175550 |
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
| Author | : Cisar Gómez |
| Publisher | : Cambridge University Press |
| Total Pages | : 477 |
| Release | : 1996-04-18 |
| Genre | : Mathematics |
| ISBN | : 0521460654 |
A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.
| Author | : Michio Jimbo |
| Publisher | : World Scientific |
| Total Pages | : 740 |
| Release | : 1990 |
| Genre | : Science |
| ISBN | : 9789810201203 |
This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.
| Author | : Michio Jimbo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 180 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803204 |
Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.
| Author | : Vyjayanthi Chari |
| Publisher | : Cambridge University Press |
| Total Pages | : 672 |
| Release | : 1995-07-27 |
| Genre | : Mathematics |
| ISBN | : 9780521558846 |
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 | : Anatoli Klimyk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 568 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642608965 |
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 | : Ian Ellery McCarthy |
| Publisher | : |
| Total Pages | : 584 |
| Release | : 1968 |
| Genre | : Science |
| ISBN | : |
Qualitative introduction -- Elastic scattering in quantum mechanics -- Nucleon-nucleon forces -- Nuclear forces in nuclear matter -- The single-particle shell model for finite nuclei -- Nuclear structure--ground states -- Nuclear structure--excited states -- Theory of nuclear reactions -- Applications of reaction theory -- Formal scattering theory -- Entrance channel phenomena -- Inelastic scattering -- Rearrangement collisions -- Breakup reactions -- Appendix 1. Units and constants -- Appendix 2. Mass defects and spins of nuclei -- Appendix 3. Functions used in potential scattering -- Appendix 4. Angular momentum.
