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C*-pseudo-multiplicative unitaries, Hopf C*-bimodules and their Fourier algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  04 February 2011

Thomas Timmermann
Thomas Timmermann
Affiliation:
Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany (timmermt@math.uni-muenster.de)
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Abstract

We introduce C*-pseudo-multiplicative unitaries and concrete Hopf C*-bimodules for the study of quantum groupoids in the setting of C*-algebras. These unitaries and Hopf C*-bimodules generalize multiplicative unitaries and Hopf C*-algebras and are analogues of the pseudo-multiplicative unitaries and Hopf–von Neumann-bimodules studied by Enock, Lesieur and Vallin. To each C*-pseudo-multiplicative unitary, we associate two Fourier algebras with a duality pairing and in the regular case two Hopf C*-bimodules. The theory is illustrated by examples related to locally compact Hausdorff groupoids. In particular, we obtain a continuous Fourier algebra for a locally compact Hausdorff groupoid.

Keywords

quantum groupoidgroupoidduality

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 1 , January 2012 , pp. 189 - 220
Copyright
Copyright © Cambridge University Press 2011

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