Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups / Edition 1

by J.L. Bueso, Josï Gïmez-Torrecillas, A. Verschoren

Overview

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.

Product Details

ISBN-13:	9781402014024
Publisher:	Springer Netherlands
Publication date:	07/31/2003
Series:	Mathematical Modelling: Theory and Applications , #17
Edition description:	2003
Pages:	300
Product dimensions:	6.14(w) x 9.21(h) x 0.03(d)

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.