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arXiv · 2406.06179

Operator-Valued Twisted Araki-Woods Algebras

Rahul Kumar R·Melchior Wirth
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Abstract

We introduce operator-valued twisted Araki-Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes $q$-Gaussian and $q$-Araki-Woods algebras and also generalize Shlyakhtenko's von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki-Woods algebras over type I factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee that factoriality of these algebras.

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BibTeXRIS

Rahul Kumar R, Melchior Wirth. 2024-06-10. Operator-Valued Twisted Araki-Woods Algebras. https://arxiv.org/abs/2406.06179

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