Algorithmic Methods in Non-Commutative Algebra

Applications to Quantum Groups

  • José Bueso
  • José Gómez-Torrecillas
  • Alain Verschoren

Part of the Mathematical Modelling book series (MMTA, volume 17)

Table of contents

  1. Front Matter
    Pages i-xi
  2. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 1-61
  3. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 63-108
  4. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 109-135
  5. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 137-168
  6. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 169-202
  7. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 203-237
  8. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 239-261
  9. José Bueso, José Gómez-Torrecillas, Alain Verschoren
    Pages 263-287
  10. Back Matter
    Pages 289-300

About this book

Introduction

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.

Keywords

Algebraic structure Gröbner basis algorithms complexity ring theory

Authors and affiliations

  • José Bueso
    • 1
  • José Gómez-Torrecillas
    • 1
  • Alain Verschoren
    • 2
  1. 1.University of GranadaGranadaSpain
  2. 2.University of AntwerpAntwerpBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0285-0
  • Copyright Information Springer Science+Business Media B.V. 2003
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6328-1
  • Online ISBN 978-94-017-0285-0
  • Series Print ISSN 1386-2960
  • About this book