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- Jean Renault, Jean Renault
- 2008

According to J. Feldman and C. Mooreâ€™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 gaveâ€¦ (More)

- ALEXANDER KUMJIAN, PAUL S. MUHLY, Jean Renault, Dana P. Williams
- 1997

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, Î±) consisting of an elementary Câˆ—-bundle A over G satisfying Fellâ€™s condition and an action Î± of G on A by âˆ—-isomorphisms. When G is the transformation groupoid X Ã—H , then Br(G) is the equivariant Brauer group BrH(X). Inâ€¦ (More)

- Jean Renault
- 2000

The usual crossed product construction which associates to the homeomorphism T of the locally compact space X the Câˆ—-algebra Câˆ—(X, T ) is extended to the case of a partial local homeomorphism T . For example, the Cuntz-Krieger algebras are the Câˆ—-algebras of the one-sided Markov shifts. The generalizations of the Cuntz-Krieger algebras (graph algebras,â€¦ (More)

Given a semigroup of local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the first named author. Under suitable hypotheses we may also define a transformation groupoid whose C*-algebra turns out to beâ€¦ (More)

- Jean Renault
- 2001

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 givenâ€¦ (More)

- Jean Renault
- 2009

This paper illustrates the notion of a Cartan subalgebra in a C*algebra through a number of examples and counterexamples. Some of these examples have a geometrical flavour and are related to orbifolds and nonHausdorff manifolds.

- Jean Renault, Marc Rieffel
- 2014

We review various notions of correspondences for locally compact groupoids with Haar systems, in particular a recent definition due to R.D. Holkar. We give the construction of the representations induced by such a correspondence. Finally, we extend the construction of induced representations to hypergroupoids.

The classical Hausdorff-Young inequality for locally compact abelian groups states that, for 1 â‰¤ p â‰¤ 2, the L-norm of a function dominates the L-norm of its Fourier transform, where 1/p + 1/q = 1. By using the theory of non-commutative L-spaces and by reinterpreting the Fourier transform, R. Kunze (1958) [resp. M. Terp (1980)] extended this inequality toâ€¦ (More)

Given a semigroup of surjective local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the first named author. We may also define a transformation groupoid whose C*-algebra turns out to be isomorphic toâ€¦ (More)

- Jean Renault
- 2002

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 gaveâ€¦ (More)