From Hopf C*-families to concrete Hopf C*-bimodules

Details From Hopf C*-families to concrete Hopf C*-bimodules From Hopf C*-families to concrete Hopf C*-bimodules

2007-12-21

arxiv.org/abs/0712.3695v1

Mathematics

Operator Algebras

29 pages

Scientific paper

In the setting of von Neumann algebras, measurable quantum groupoids have successfully been axiomatized and studied by Enock, Vallin, and Lesieur, whereas in the setting of $C^{*}$-algebras, a similar theory of locally compact quantum groupoids could not yet be developed. Some basic building blocks for such a theory, like analogues of a Hopf-von Neumann bimodule and of a pseudo-multiplicative unitary, were introduced in the thesis and a recent article by the author. That approach, however, is restricted to decomposable quantum groupoids which generalize $r$-discrete groupoids. Recently, we developed a general approach that covers all locally compact groupoids. In this article, we explain how the special theory of our thesis embeds into the general one.

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