Operator-Valued Twisted Araki-Woods Algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910545301471232 |
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| author | R, Rahul Kumar Wirth, Melchior |
| author_facet | R, Rahul Kumar Wirth, Melchior |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator-Valued Twisted Araki-Woods Algebras R, Rahul Kumar Wirth, Melchior Operator Algebras Mathematical Physics Functional Analysis 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. |
| title | Operator-Valued Twisted Araki-Woods Algebras |
| topic | Operator Algebras Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2406.06179 |