1. Operator-Valued Twisted Araki-Woods Algebras
- Author
-
R, Rahul Kumar and Wirth, Melchior
- Subjects
Mathematics - Operator Algebras ,Mathematical Physics ,Mathematics - Functional Analysis - 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.
- Published
- 2024