In two articles ([L2], [L3]), Franck Lesieur had introduced a notion ofquantum groupoid, in the setting of von Neumann algebras, using intensively thenotion of pseudo-multiplicative unitary, which had been introduced in aprevious 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 ofC*-algebras. This allows us to re-use as quantum groupoids some examplesintroduced by Etienne Blanchard.
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