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arXiv · 1605.06057

Classification of a family of non almost periodic free Araki-Woods factors

Cyril Houdayer·Dimitri Shlyakhtenko·Stefaan Vaes
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Abstract

We obtain a complete classification of a large class of non almost periodic free Araki-Woods factors $Γ(μ,m)"$ up to isomorphism. We do this by showing that free Araki-Woods factors $Γ(μ, m)"$ arising from finite symmetric Borel measures $μ$ on $\mathbf{R}$ whose atomic part $μ_a$ is nonzero and not concentrated on $\{0\}$ have the joint measure class $\mathcal C(\bigvee_{k \geq 1} μ^{\ast k})$ as an invariant. Our key technical result is a deformation/rigidity criterion for the unitary conjugacy of two faithful normal states. We use this to also deduce rigidity and classification theorems for free product von Neumann algebras.

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Cyril Houdayer, Dimitri Shlyakhtenko, Stefaan Vaes. 2017-02-24. Classification of a family of non almost periodic free Araki-Woods factors. https://doi.org/10.4171/jems%2F898

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