We obtain a complete classification of a large class of non-almost-periodic free Araki–Woods factors up to isomorphism. We do this by showing that free Araki–Woods factors arising from finite symmetric Borel measures on whose atomic part is nonzero and not concentrated on have the joint measure class 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 L. Shlyakhtenko, Stefaan Vaes, Classification of a family of non-almost-periodic free Araki–Woods factors. J. Eur. Math. Soc. 21 (2019), no. 10, pp. 3113–3142DOI 10.4171/JEMS/898