Operator-valued twisted Araki–Woods algebras
Kumar RR, Wirth M. 2025. Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. 406(5), 110.
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Author
Kumar, R. Rahul;
Wirth, MelchiorISTA 
Corresponding author has ISTA affiliation
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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 the factoriality of these algebras.
Publishing Year
Date Published
2025-05-01
Journal Title
Communications in Mathematical Physics
Publisher
Springer Nature
Acknowledgement
The authors want to thank the organizers of YMC*A 2023 in Leuven, where this collaboration was conceived. They are grateful to Dan Voiculescu for a valuable historical remark and to Zhiyuan Yang for raising the question if operator-valued weights give rise to Tomita correspondences. R.K. was funded by IIT Kanpur through the Institute Postdoctoral Fellowship. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.
Open Access funding enabled and organized by Projekt DEAL.
Volume
406
Issue
5
Article Number
110
ISSN
eISSN
IST-REx-ID
Cite this
Kumar RR, Wirth M. Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. 2025;406(5). doi:10.1007/s00220-025-05285-7
Kumar, R. R., & Wirth, M. (2025). Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-025-05285-7
Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” Communications in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s00220-025-05285-7.
R. R. Kumar and M. Wirth, “Operator-valued twisted Araki–Woods algebras,” Communications in Mathematical Physics, vol. 406, no. 5. Springer Nature, 2025.
Kumar RR, Wirth M. 2025. Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. 406(5), 110.
Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” Communications in Mathematical Physics, vol. 406, no. 5, 110, Springer Nature, 2025, doi:10.1007/s00220-025-05285-7.
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