Type III factors with unique Cartan decomposition

Details Type III factors with unique Cartan decomposition Type III factors with unique Cartan decomposition

2012-03-06

arxiv.org/abs/1203.1254v2

Mathematics

Operator Algebras

v2: we only fixed a LaTeX issue

Scientific paper

We prove that for any free ergodic nonsingular nonamenable action \Gamma\ \actson (X,\mu) of all \Gamma\ in a large class of groups including all hyperbolic groups, the associated group measure space factor $L^\infty(X) \rtimes \Gamma$ has L^\infty(X) as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in [PV12]. We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products $M_1 *_B M_2$ over a subalgebra B of type I.

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