Type III factors with unique Cartan decomposition |
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Authors: | Cyril Houdayer Stefaan Vaes |
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Institution: | 1. CNRS-ENS Lyon, UMPA UMR 5669, 69364 Lyon cedex 7, France;2. KU Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium |
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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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Keywords: | 46L10 46L54 37A40 |
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