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

  • Book
  • © 1997

Overview

Authors:
  1. Larry A. Lambe

    1. CAIP, Rutgers University, Piscataway, USA
      University of Wales, Bangor, Bangor, Gwynedd, UK

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    You can also search for this author in PubMed   Google Scholar

  2. David E. Radford

    1. University of Illinois at Chicago, Chicago, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 423)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Algebraic Preliminaries

    • Larry A. Lambe, David E. Radford
    Pages 1-63

  3. The Quantum Yang-Baxter Equation (QYBE)

    • Larry A. Lambe, David E. Radford
    Pages 65-86

  4. Categories of Quantum Yang-Baxter Modules

    • Larry A. Lambe, David E. Radford
    Pages 87-120

  5. More on the Bialgebra Associated to the Quantum Yang-Baxter Equation

    • Larry A. Lambe, David E. Radford
    Pages 121-142

  6. The Fundamental Example of a Quantum Group

    • Larry A. Lambe, David E. Radford
    Pages 143-160

  7. Quasitriangular Algebras, Bialgebras, Hopf Algebras and The Quantum Double

    • Larry A. Lambe, David E. Radford
    Pages 161-195

  8. Coquasitriangular Structures

    • Larry A. Lambe, David E. Radford
    Pages 197-218

  9. Some Classes of Solutions

    • Larry A. Lambe, David E. Radford
    Pages 219-248

  10. Categorical Constructions and Generalizations of the Quantum Yang-Baxter Equation

    • Larry A. Lambe, David E. Radford
    Pages 249-260

  11. Back Matter

    Pages 261-299
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Keywords

About this book

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.

Authors and Affiliations

  • CAIP, Rutgers University, Piscataway, USA

    Larry A. Lambe

  • University of Wales, Bangor, Bangor, Gwynedd, UK

    Larry A. Lambe

  • University of Illinois at Chicago, Chicago, USA

    David E. Radford

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