Measured Quantum Groupoids in action
| dc.creator | Enock, Michel | |
| dc.date | 2007-10-29 | |
| dc.date | 2008-09-19 | |
| dc.date.accessioned | 2026-07-07T10:03:34Z | |
| dc.date.available | 2026-07-07T10:03:34Z | |
| dc.description | Franck Lesieur had introduced in his thesis (now published in an expended and revised version in the {\it Mémoires de la SMF} (2007)) a notion of measured quantum groupoid, in the setting of von Neumann algebras and a simplification of Lesieur's axioms is presented in an appendix of this article. We here develop the notions of actions, crossed-product, and obtain a biduality theorem, following what had been done by Stefaan Vaes for locally compact quantum groups. Moreover, we prove that the inclusion of the initial algebra into its crossed-product is depth 2, which gives a converse of a result proved by Jean-Michel Vallin and the author. More precisely, to any action of a measured quantum groupoid, we associate another measured quantum groupoid. In particular, starting from an action of a locally compact quantum group, we obtain a measured quantum groupoid canonically associated to this action; when the action is outer, this measured quantum groupoid is the initial locally compact quantum group | |
| dc.description | will be published in {\it Mémoires SMF}, 2009 | |
| dc.identifier | https://arxiv.org/abs/0710.5364 | |
| dc.identifier | http://arxiv.org/abs/0710.5364 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169335 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55; 46L89 | |
| dc.title | Measured Quantum Groupoids in action | |
| dc.type | text |