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

Thomas Timmermann

doi:10.1017/S1474748010000290

C-pseudo-multiplicative unitaries and Hopf C-bimodules

Operator Algebras 2013-07-02 v1 Quantum Algebra

Authors: 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.

Keywords

c*-algebra hilbert modules hopf algebras

Cite

@article{arxiv.0908.1850,
  title  = {C*-pseudo-multiplicative unitaries and Hopf C*-bimodules},
  author = {Thomas Timmermann},
  journal= {arXiv preprint arXiv:0908.1850},
  year   = {2013}
}

Comments

50 pages; this is a substantial revision and expansion of the preprint "C*-pseudo-multiplicative unitaries" (arXiv:0709.2995) with many new results