The Unitary Implementation of a Measured Quantum Groupoid action

Details The Unitary Implementation of a Measured Quantum Groupoid action The Unitary Implementation of a Measured Quantum Groupoid action

2008-08-29

arxiv.org/abs/0808.4049v2

Mathematics

Operator Algebras

to be published in "Annales Mathematiques Blaise Pascal"

Scientific paper

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 notion of actions, crossed-product, dual actions of a measured quantum groupoid: a biduality theorem for actions had been proved. This article continues that program : we prove the existence of a standard implementation for an action, and a bidulaity 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.

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