The unitary implementation of a measured quantum groupoid action

Michel Enock[1]

  • [1] Institut de Mathématiques de Jussieu, UMR 7586 du CNRS, Paris 6 & Paris 7 175, rue du Chevaleret, Plateau 7E, F-75013 Paris France

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 2, page 233-302
  • ISSN: 1259-1734

Abstract

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Mimicking the von Neumann version of Kustermans and Vaes’ locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In a former article, the author had introduced the notions of actions, crossed-product, dual actions of a measured quantum groupoid; a biduality theorem for actions has been proved. This article continues that program: we prove the existence of a standard implementation for an action, and a biduality theorem for weights. We generalize this way results which were proved, for locally compact quantum groups by S. Vaes, and for measured groupoids by T. Yamanouchi.

How to cite

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Enock, Michel. "The unitary implementation of a measured quantum groupoid action." Annales mathématiques Blaise Pascal 17.2 (2010): 233-302. <http://eudml.org/doc/116353>.

@article{Enock2010,
abstract = {Mimicking the von Neumann version of Kustermans and Vaes’ locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In a former article, the author had introduced the notions of actions, crossed-product, dual actions of a measured quantum groupoid; a biduality theorem for actions has been proved. This article continues that program: we prove the existence of a standard implementation for an action, and a biduality theorem for weights. We generalize this way results which were proved, for locally compact quantum groups by S. Vaes, and for measured groupoids by T. Yamanouchi.},
affiliation = {Institut de Mathématiques de Jussieu, UMR 7586 du CNRS, Paris 6 & Paris 7 175, rue du Chevaleret, Plateau 7E, F-75013 Paris France},
author = {Enock, Michel},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Measured quantum groupoids; actions; biduality theorems; measured quantum groupoids},
language = {eng},
month = {7},
number = {2},
pages = {233-302},
publisher = {Annales mathématiques Blaise Pascal},
title = {The unitary implementation of a measured quantum groupoid action},
url = {http://eudml.org/doc/116353},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Enock, Michel
TI - The unitary implementation of a measured quantum groupoid action
JO - Annales mathématiques Blaise Pascal
DA - 2010/7//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 2
SP - 233
EP - 302
AB - Mimicking the von Neumann version of Kustermans and Vaes’ locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In a former article, the author had introduced the notions of actions, crossed-product, dual actions of a measured quantum groupoid; a biduality theorem for actions has been proved. This article continues that program: we prove the existence of a standard implementation for an action, and a biduality theorem for weights. We generalize this way results which were proved, for locally compact quantum groups by S. Vaes, and for measured groupoids by T. Yamanouchi.
LA - eng
KW - Measured quantum groupoids; actions; biduality theorems; measured quantum groupoids
UR - http://eudml.org/doc/116353
ER -

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