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arXiv · 1810.01924

Free products of finite-dimensional and other von Neumann algebras in terms of free Araki-Woods factors

Michael Hartglass·Brent Nelson
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Abstract

We show that any free product of finite-dimensional von Neumann algebras equipped with non-tracial states is isomorphic to a free Araki-Woods factor with its free quasi-free state possibly direct sum a finite-dimensional von Neumann algebra. This gives a complete answer to questions posed by Dykema and Shlyakhtenko, which had been partially answered by work of Houdayer and work of Ueda. We also extend this to suitable infinite-dimensional von Neumann algebras with almost periodic states.

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Michael Hartglass, Brent Nelson. 2018-10-03. Free products of finite-dimensional and other von Neumann algebras in terms of free Araki-Woods factors. https://arxiv.org/abs/1810.01924

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