Jean Renault

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According to J. Feldman and C. Moore’s wellknown theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e., a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave(More)
Abstract. We define the Brauer group Br(G) of a locally compact groupoid G to be the set of Morita equivalence classes of pairs (A, α) consisting of an elementary C∗-bundle A over G satisfying Fell’s condition and an action α of G on A by ∗-isomorphisms. When G is the transformation groupoid X ×H , then Br(G) is the equivariant Brauer group BrH(X). In(More)
The usual crossed product construction which associates to the homeomorphism T of the locally compact space X the C∗-algebra C∗(X, T ) is extended to the case of a partial local homeomorphism T . For example, the Cuntz-Krieger algebras are the C∗-algebras of the one-sided Markov shifts. The generalizations of the Cuntz-Krieger algebras (graph algebras,(More)
After a review of some the main results about hyperfinite equivalence relations and their cocycles in the measured setting, we give a definition of a topological AF equivalence relation. We show that every cocycle is cohomologous to a quasi-product cocycle. We then study the problem of determining the quasi-invariant probability measures admitting a given(More)
According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e. a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave(More)