Strong solidity of free Araki-Woods factors
arXiv:1512.04820 · doi:10.1353/ajm.2018.0029
Abstract
We show that Shlyakhtenko's free Araki-Woods factors are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expectation, the normalizer remains amenable. This provides the first class of nonamenable strongly solid type III factors.
v2: minor changes, final version, to appear in American Journal of Mathematics
References in corpus (6)
- On a Class of Type II Factors with Betti Numbers Invariants
- Unique prime factorization and bicentralizer problem for a class of type III factors
- Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
- Asymptotic structure of free product von Neumann algebras
- Asymptotic structure of free Araki-Woods factors
- 1-bounded entropy and regularity problems in von Neumann algebras
Cited by in corpus (7)
- On the factoriality of q-deformed Araki-Woods von Neumann algebras
- Complete metric approximation property for -Araki-Woods algebras
- Structure of extensions of free Araki-Woods factors
- Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras
- Cartan subalgebras in C*-algebras. Existence and uniqueness
- Crossed-products by locally compact groups: Intermediate subfactors
- Riesz transforms on compact quantum groups and strong solidity