Inclusions of von Neumann Algebras and Quantum groupoids III
Michel Enock
Abstract
In a former article, in collaboration with Jean-Michel Vallin, we have constructed two "quantum groupo\"ıds" 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 groupo\"ıds".
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