More than 1,900 Springer Protocols eBooks at just $9.99 each! Get yours today>>

Mathematics and Its Applications

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

Authors: Lambe, L.A., Radford, D.E.

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4615-4109-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-0-7923-4721-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4613-6842-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

Table of contents (9 chapters)

  • Algebraic Preliminaries

    Lambe, Larry A. (et al.)

    Pages 1-63

  • The Quantum Yang-Baxter Equation (QYBE)

    Lambe, Larry A. (et al.)

    Pages 65-86

  • Categories of Quantum Yang-Baxter Modules

    Lambe, Larry A. (et al.)

    Pages 87-120

  • More on the Bialgebra Associated to the Quantum Yang-Baxter Equation

    Lambe, Larry A. (et al.)

    Pages 121-142

  • The Fundamental Example of a Quantum Group

    Lambe, Larry A. (et al.)

    Pages 143-160

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4615-4109-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-0-7923-4721-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4613-6842-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Services for this Book

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach
Authors
Series Title
Mathematics and Its Applications
Series Volume
423
Copyright
1997
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4615-4109-7
DOI
10.1007/978-1-4615-4109-7
Hardcover ISBN
978-0-7923-4721-7
Softcover ISBN
978-1-4613-6842-7
Edition Number
1
Number of Pages
XX, 300
Topics