Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups
About the 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 Poincare-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.
Book Details
ISBN-13: 9781402014024
EAN: 9781402014024
Publisher Date: 31 Jul 2003
Dewey: 512.55
Illustration: Y
LCCN: 2003052014
No of Pages: 300
Returnable: N
Spine Width: 20 mm
ISBN-10: 1402014023
Publisher: Springer
Binding: Hardcover
Height: 235 mm
Language: English
MediaMail: Y
PrintOnDemand: N
Series Title: English
Width: 160 mm