Type III factors with unique Cartan decomposition
By Cyril Houdayer, S. Vaes. 2012
65 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bbe611b8fc60045c8684b14cfc5f0ba8a6eacbdd
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Unique prime factorization and bicentralizer problem for a class of type III factors (2015, unknown): “Then we can proceed as in the proof of [Ue12, Proposition 3.1 (i) ⇒ (ii) ⇒ (iii)] (see also [HV12, Theorem 2.3 (2) ⇒ (1)]) and we deduce that A (cid:22) M q 0 B 1 q 0 .”
- Examples of factors which have no Cartan subalgebras (2012, background): “ E. To prove Theorem A, we need only slight modifications of the proof of (a special case of) [27,Theorem 3.1]. Theorem B can be proved by seeing its continuous core, and this idea comes from [16] and [17]. Since condition (AOC)+ is similar to condition (AO) with respect to the continuous core, we na”