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Other literature type . 1995
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Communications in Mathematical Physics
Article . 1995 . Peer-reviewed
License: Springer TDM
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zbMATH Open
Article . 1995
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Non-compact quantum groups associated with Abelian subgroups

Authors: Rieffel, Marc A.;

Non-compact quantum groups associated with Abelian subgroups

Abstract

Soit \(G\) un groupe de Lie d'algèbre de Lie \({\mathfrak g}\) et soit \({\mathfrak h}\) une sous-algèbre de Lie abélienne de \({\mathfrak g}\). Au début de cet article l'auteur rappelle comment on peut associer à tout \(r\) dans \({\mathfrak h}\wedge{\mathfrak h}\) une structure de Poisson compatible sur \(G\). Par ailleurs dans [Deformation quantization for actions of \(\mathbb{R}^d\), Mem. Am. Math. Soc. 506 (1993; Zbl 0798.46053)] l'auteur a développé une méthode de construction d'une déformation d'une \(C^*\)-algèbre dans la direction de n'importe quel crochet de Poisson provenant d'une action de \(\mathbb{R}^d\) \((d\geq 2)\). Il utilise alors cette méthode pour construire le groupe quantique associé à la structure de Poisson correspondante à \(r\in{\mathfrak h}\wedge{\mathfrak h}\). Cette quantification sera préférée, c'est-à-dire, seulement le produit des fonctions sur \(G\) sera déformé. Cette dernière construction a été détaillée dans [Contemp. Math. 145, 465-491 (1993; Zbl 0795.17017)] dans le cas où \(G\) est compact. Ce travail est intéressant car il fournit plusieurs nouveaux exemples de groupes quantiques.

Related Organizations
Keywords

58B30, 46L05, quantum groups, 46L87, deformation of \(C^*\)-algebra, Poisson structure, Quantum groups (quantized enveloping algebras) and related deformations, 17B37, 81R50, quantum deformations of compact groups, 22D25, Noncommutative differential geometry, 16W30

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
15
Average
Top 10%
Average
Green