  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.
