Continuous fields of C*-algebras and Lesieur's Quantum Groupoids

Details Continuous fields of C*-algebras and Lesieur's Quantum Groupoids Continuous fields of C*-algebras and Lesieur's Quantum Groupoids

2006-05-18

arxiv.org/abs/math/0605512v3

Mathematics

Operator Algebras

This paper had been withdrawn, and is now again available with some minor corrections

Scientific paper

In two articles ([L2], [L3]), Franck Lesieur had introduced a notion of quantum groupoid, in the setting of von Neumann algebras, using intensively the notion of pseudo-multiplicative unitary, which had been introduced in a previous article of the author, in collaboration with Jean-Michel Vallin [EV]. We are here studying the analog of Lesieur's construction in a C*-framework, when the basis of the quantum groupoid is central; in this case, the C* structure obtained can be described using the tools of continuous fields of C*-algebras. This allows us to re-use as quantum groupoids some examples introduced by Etienne Blanchard.

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