Classification of a family of non-almost-periodic free Araki-Woods factors
Open Access Publications from the University of California

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

• Author(s): Houdayer, Cyril
• Shlyakhtenko, Dimitri
• Vaes, Stefaan
• et al.

## Published Web Location

https://doi.org/10.4171/JEMS/898
Abstract

We obtain a complete classification of a large class of non almost periodic free Araki-Woods factors $\Gamma(\mu,m)"$ up to isomorphism. We do this by showing that free Araki-Woods factors $\Gamma(\mu, m)"$ arising from finite symmetric Borel measures $\mu$ on $\mathbf{R}$ whose atomic part $\mu_a$ is nonzero and not concentrated on $\{0\}$ have the joint measure class $\mathcal C(\bigvee_{k \geq 1} \mu^{\ast k})$ 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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