Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups
Author:   J.L. Bueso ,  José Gómez-Torrecillas ,  A. Verschoren
Publisher:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   17
ISBN:  

9781402014024


Pages:   300
Publication Date:   31 July 2003
Format:   Hardback
Availability:   In Print   Availability explained
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Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups


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Overview

The already broad range of applications of ring theory has been enhanced in the 1980s 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 co-ordinate 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 Poincare-Birkhoff-Witt rings. Included are 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, and so on.

Full Product Details

Author:   J.L. Bueso ,  José Gómez-Torrecillas ,  A. Verschoren
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   17
Dimensions:   Width: 15.60cm , Height: 1.90cm , Length: 23.40cm
Weight:   1.370kg
ISBN:  

9781402014024


ISBN 10:   1402014023
Pages:   300
Publication Date:   31 July 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

1. Generalities on rings.- 2. Gröbner basis computation algorithms.- 3. Poincaré-Birkhoff-Witt Algebras.- 4. First applications.- 5. Gröbner bases for modules.- 6. Syzygies and applications.- 7. The Gelfand-Kirillov dimension and the Hilbert polynomial.- 8. Primality.- References.

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