Abstract
We prove that for any free ergodic nonsingular nonamenable action Γ↷(X,μ) of all Γ in a large class of groups including all hyperbolic groups, the associated group measure space von Neumann algebra L∞(X)⋊Γ has L∞(X) as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in Popa and Vaes (in press) [38]. We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products M1⁎BM2 over a subalgebra B of type I.
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