Strong solidity of free Araki-Woods factors
R\'emi Boutonnet, Cyril Houdayer, Stefaan Vaes
TL;DR
This paper proves that free Araki-Woods factors, a class of nonamenable type III von Neumann algebras, are strongly solid, meaning their normalizers of diffuse amenable subalgebras are also amenable, marking a significant advancement in operator algebra theory.
Contribution
It establishes the strong solidity of free Araki-Woods factors, the first known class of nonamenable strongly solid type III factors, expanding understanding of their structural properties.
Findings
Free Araki-Woods factors are strongly solid.
Normalizers of diffuse amenable subalgebras are amenable.
First nonamenable strongly solid type III factors identified.
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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Holomorphic and Operator Theory · Geometry and complex manifolds