Abstract :
In a former article, in collaboration with Jean–Michel Vallin, we have constructed two
“quantum groupoïds” dual to each other, from a depth 2 inclusion of von Neumann algebras
M0 ⊂ M1, in such a way that the canonical Jones’tower associated to the inclusion can be
described as a tower of successive crossed-products by these two structures. We are now
investigating in greater details these structures in the presence of an appropriate modular theory
on the basis M 0 ∩M1, and we show how these examples fit with Lesieur’s “measured quantum
groupoïds”.
© 2005 Elsevier Inc. All rights reserved.
