Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups (Hardback or Cased Book)

Bueso, J. L.

ISBN 10: 1402014023 / ISBN 13: 9781402014024

Published by Springer 7/31/2003, 2003

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Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups.

Seller Inventory # BBS-9781402014024

Bibliographic Details

• Title: Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups (Hardback or Cased Book)
• Publisher: Springer 7/31/2003
• Publication Date: 2003
• Language: English
• ISBN 10: 1402014023
• ISBN 13: 9781402014024
• Binding: Hardback or Cased Book
• Condition: New
• Weight: 1.35 pounds
• Book Type: Book

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Synopsis

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.