Titre: Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups (Mathematical Modelling: Theory and Applications)
�diteur: Springer
Date de parution: 2010
Langue: anglais
ISBN � 10 chiffres: 9048163285
ISBN � 13 chiffres: 9789048163281
Reliure: Couverture souple
�tat de l'article: New

A propos de ce titre

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 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.

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