Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach

Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach PDF Author: L.A. Lambe
Publisher: Springer Science & Business Media
ISBN: 1461541093
Category : Mathematics
Languages : en
Pages : 314

Get Book Here

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.

Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach

Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach PDF Author: L.A. Lambe
Publisher: Springer Science & Business Media
ISBN: 1461541093
Category : Mathematics
Languages : en
Pages : 314

Get Book Here

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.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations

Hopf Algebras, Quantum Groups and Yang-Baxter Equations PDF Author: Florin Felix Nichita
Publisher: MDPI
ISBN: 3038973246
Category : Mathematics
Languages : en
Pages : 239

Get Book Here

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

Representations of the Infinite Symmetric Group

Representations of the Infinite Symmetric Group PDF Author: Alexei Borodin
Publisher: Cambridge University Press
ISBN: 1107175550
Category : Mathematics
Languages : en
Pages : 169

Get Book Here

Book Description
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.

Lectures on Algebraic Quantum Groups

Lectures on Algebraic Quantum Groups PDF Author: Ken Brown
Publisher: Birkhäuser
ISBN: 303488205X
Category : Mathematics
Languages : en
Pages : 339

Get Book Here

Book Description
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Quantum Groups in Two-Dimensional Physics

Quantum Groups in Two-Dimensional Physics PDF Author: Cisar Gómez
Publisher: Cambridge University Press
ISBN: 0521460654
Category : Mathematics
Languages : en
Pages : 477

Get Book Here

Book Description
A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.

Quantum Groups and Their Representations

Quantum Groups and Their Representations PDF Author: Anatoli Klimyk
Publisher: Springer Science & Business Media
ISBN: 3642608965
Category : Science
Languages : en
Pages : 568

Get Book Here

Book Description
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.

Encyclopedia of Knot Theory

Encyclopedia of Knot Theory PDF Author: Colin Adams
Publisher: CRC Press
ISBN: 1000222381
Category : Education
Languages : en
Pages : 954

Get Book Here

Book Description
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Yang-Baxter Equation in Integrable Systems

Yang-Baxter Equation in Integrable Systems PDF Author: Michio Jimbo
Publisher: World Scientific
ISBN: 9789810201210
Category : Science
Languages : en
Pages : 740

Get Book Here

Book Description
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.

Hopf Algebras, Tensor Categories and Related Topics

Hopf Algebras, Tensor Categories and Related Topics PDF Author: Nicolás Andruskiewitsch
Publisher: American Mathematical Soc.
ISBN: 1470456249
Category : Education
Languages : en
Pages : 372

Get Book Here

Book Description
The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.

Hopf Algebras

Hopf Algebras PDF Author: David E Radford
Publisher: World Scientific
ISBN: 9814405108
Category : Mathematics
Languages : en
Pages : 584

Get Book Here

Book Description
The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.