Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups
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Book 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 Poincar -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.
Format:Paperback
Language:English
ISBN:9048163285
ISBN13:9789048163281
Release Date:December 2010
Publisher:Springer
Length:300 Pages
Weight:0.98 lbs.
Dimensions:0.7" x 6.1" x 9.2"
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