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arXiv · 0908.1850

C*-pseudo-multiplicative unitaries and Hopf C*-bimodules

Thomas Timmermann
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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-bimod-ules studied by Enock, Lesieur and Vallin. To each C*-pseudo-multiplicative unitary, we associate two Fourier algebras with a duality pairing, a C*-tensor category of representations, and in the regular case two reduced and two universal 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.

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Thomas Timmermann. 2009-08-13. C*-pseudo-multiplicative unitaries and Hopf C*-bimodules. https://doi.org/10.1017/s1474748010000290

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