Apparaît dans la collection : Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette

I present a joint work with Sorin Popa and Dimitri Shlyakhtenko. We prove that under a natural condition, the regular von Neumann subalgebras B of the hyperfinite II1 factor R are completely classified (up to conjugacy by an automorphism of R) by theassociated discrete measured groupoid. We obtain a similar result for triple inclusions of A in B in R, where A is a Cartan subalgebra in R and the intermediate von Neumann algebraB is regular in R. The two key steps in proving these results are the vanishing of the 2-cohomology for cocycle actions of amenable discrete measured groupoids and the approximate vanishing of the 1-cohomology.