Inclusions of von Neumann Algebras and Quantum groupoids III

Details Inclusions of von Neumann Algebras and Quantum groupoids III Inclusions of von Neumann Algebras and Quantum groupoids III

2004-05-25

arxiv.org/abs/math/0405480v1

Mathematics

Operator Algebras

Scientific paper

In a former article, in collaboration with Jean-Michel Vallin, we have constructed two "quantum groupo\"{\i}ds" dual to each other, from a depth 2 inclusion of von Neumann algebras $M_0\subset M_1$, 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 $M'_0\cap M_1$, and we show how these examples fit with Lesieur's "measured quantum groupo\"{\i}ds".

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