A new characterisation of idempotent states on finite and compact quantum groups

Uwe Franz; Adam Skalski

doi:10.1016/j.crma.2009.06.015

Algebra/Functional Analysis

A new characterisation of idempotent states on finite and compact quantum groups

Presented by: Gilles Pisier

Uwe Franz ¹; Adam Skalski ²

¹ Département de mathématiques de Besançon, Université de Franche-Comté, 16, route de Gray, 25030 Besançon, France
² Department of Mathematics and Statistics, Lancaster University, Lancaster, United Kingdom

Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 991-996.

Abstract
Résumé

We show that idempotent states on finite quantum groups correspond to pre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows that the lattices formed by the idempotent states on a finite quantum group and by its coidalgebras are isomorphic. We show, furthermore, that these lattices are also isomorphic for compact quantum groups, if one restricts to expected coidalgebras.

Nous donnons une caractérisation des états idempotents sur un groupe quantique fini en termes des pré-sous-groupes introduits par Baaj, Blanchard, et Skandalis, et en déduisons un isomorphisme entre le réseau des états idempotents et le réseau des sous-algèbres coïdéales d'un groupe quantique fini. Cet isomorphisme s'étend aux groupes quantiques compacts, si on le restreind au sous-algèbres coïdéales expectées.

Received: 2009-06-02
Accepted: 2009-06-25
Published online: 2009-07-22

DOI: 10.1016/j.crma.2009.06.015

Author's affiliations:

Uwe Franz ¹; Adam Skalski ²

¹ Département de mathématiques de Besançon, Université de Franche-Comté, 16, route de Gray, 25030 Besançon, France
² Department of Mathematics and Statistics, Lancaster University, Lancaster, United Kingdom

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Uwe Franz; Adam Skalski. A new characterisation of idempotent states on finite and compact quantum groups. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 991-996. doi : 10.1016/j.crma.2009.06.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.015/

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