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

Bueso, J.L.; Gómez-Torrecillas, José; Verschoren, A.

 
9781402014024: Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups
Couverture rigide
ISBN 10 : 1402014023 ISBN 13 : 9781402014024
Editeur : Kluwer Academic Publishers, 2003

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Kluwer Academic Publishers
Date d'édition
2003
Langue
anglais
ISBN 10 
1402014023
ISBN 13 
9781402014024
Reliure
Relié
Nombre de pages
300
Coordonnées du fabricant
non disponible
Personne responsable
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Autres éditions populaires du même titre

9789048163281: Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups

Edition présentée

ISBN 10 :  9048163285 ISBN 13 :  9789048163281
Editeur : Springer, 2010
Couverture souple