Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups
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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
Width: 160 mm
ISBN-10: 1402014023
Publisher: Springer
Binding: Hardcover
Height: 235 mm
Language: English
MediaMail: Y
PrintOnDemand: Y
Series Title: English
Weight: 613 gr
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