Algorithmic Methods in Non-Commutative Algebra [electronic resource] : Applications to Quantum Groups /

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.

Bibliographic Details

Main Authors:	Bueso, José. author., Gómez-Torrecillas, José. author., Verschoren, Alain. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 2003
Subjects:	Computer science., Numerical analysis., Algebraic geometry., Associative rings., Rings (Algebra)., Category theory (Mathematics)., Homological algebra., Algorithms., Computer Science., Numeric Computing., Associative Rings and Algebras., Category Theory, Homological Algebra., Algebraic Geometry.,
Online Access:	http://dx.doi.org/10.1007/978-94-017-0285-0
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