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Classification of free Araki-Woods factors

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OASW01 - Structure of operator algebras: subfactors and fusion categories

Co-authors: Cyril Houdayer (Université Paris Sud) and Dimitri Shlyakhtenko (UCLA).
Free Araki-Woods factors are a free probability analog of the type III hyperfinite factors. They were introduced by Shlyakhtenko in 1996, who completely classified the free Araki-Woods factors associated with almost periodic orthogonal representations of the real numbers. I present a joint work with Houdayer and Shlyakhtenko in which we completely classify a large class of non almost periodic free Araki-Woods factors. The key technical result is a deformation/rigidity criterion for the unitary conjugacy of two faithful normal states on a von Neumann algebra.

This talk is part of the Isaac Newton Institute Seminar Series series.

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