Mathematical Modelling: Theory and Applications

Algorithmic Methods in Non-Commutative Algebra

Applications to Quantum Groups

Authors: Bueso, J.L., Gómez-Torrecillas, José, Verschoren, A.

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eBook $109.00
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  • ISBN 978-94-017-0285-0
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About this book

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.

Table of contents (8 chapters)

  • Generalities on rings

    Bueso, José (et al.)

    Pages 1-61

  • Gröbner basis computation algorithms

    Bueso, José (et al.)

    Pages 63-108

  • Poincaré-Birkhoff-Witt Algebras

    Bueso, José (et al.)

    Pages 109-135

  • First applications

    Bueso, José (et al.)

    Pages 137-168

  • Gröbner bases for modules

    Bueso, José (et al.)

    Pages 169-202

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-94-017-0285-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4020-1402-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-90-481-6328-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algorithmic Methods in Non-Commutative Algebra
Book Subtitle
Applications to Quantum Groups
Authors
Series Title
Mathematical Modelling: Theory and Applications
Series Volume
17
Copyright
2003
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-0285-0
DOI
10.1007/978-94-017-0285-0
Hardcover ISBN
978-1-4020-1402-4
Softcover ISBN
978-90-481-6328-1
Series ISSN
1386-2960
Edition Number
1
Number of Pages
XI, 300
Topics