Type: Article
Publication Date: 2019-06-13
Citations: 8
DOI: https://doi.org/10.4171/jems/898
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 \mathbb{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.