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Media type:
E-Article
Title:
MEASURED QUANTUM GROUPOIDS WITH A CENTRAL BASIS
Contributor:
ENOCK, MICHEL
imprint:
Theta Foundation, 2011
Published in:Journal of Operator Theory
Language:
English
ISSN:
1841-7744;
0379-4024
Origination:
Footnote:
Description:
<p>Mimicking the von Neumann version of Kustermans and Vaes' locally compact quantum groups, Franck Lesieur has introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In this article, we suppose that the basis of the measured quantum groupoid is central; in that case, we prove that a specific sub-C*-algebra is invariant under all the data of the measured quantum groupoid; moreover, this sub-C*-algebra is a continuous field of C*-algebras; when the basis is central in both the measured quantum groupoid and its dual, we get that the measured quantum groupoid is a continuous field of locally compact quantum groups. On the other hand, using this sub-C*-algebra, we prove that any abelian measured quantum groupoid comes from a locally compact groupoid.</p>