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QUANTUM GROUPOIDS OF COMPACT TYPE

Published online by Cambridge University Press:  10 February 2005

Michel Enock
Michel Enock
Affiliation:
Institut de Mathématiques de Jussieu, Unité Mixte Paris 6/Paris 7, CNRS de Recherche 7586, Case 191, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France (enock@math.jussieu.fr)
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Abstract

To any groupoid, equipped with a Haar system, Jean-Michel Vallin had associated several objects (pseudo-multiplicative unitary, Hopf-bimodule) in order to generalize, up to the groupoid case, the classical notions of multiplicative unitary and Hopf–von Neumann algebra, which were intensely used to construct quantum groups in the operator algebra setting. In two former articles (one in collaboration with Jean-Michel Vallin), starting from a depth-2 inclusion of von Neumann algebras, we have constructed such objects, which allowed us to study two ‘quantum groupoids’ dual to each other. We are now investigating in greater details the notion of pseudo-multiplicative unitary, following the general strategy developed by Baaj and Skandalis for multiplicative unitaries.

AMS 2000 Mathematics subject classification: Primary 46L89; 22A22; 81R50

Keywords

C*-algebrasvon Neumann algebrasHopf-bimodulepseudo-multiplicative unitaryquantum groupoid
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 4 , Issue 1 , January 2005 , pp. 29 - 133
Copyright
2005 Cambridge University Press

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Footnotes

Please note that the DOIs in the printed edition of volume 4 issue 1 contained errors. Correct DOIs for each article in this issue are published here online. We apologise for any inconvenience caused