Operator-Valued Twisted Araki-Woods Algebras
Operator Algebras
2024-07-30 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We introduce operator-valued twisted Araki-Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes -Gaussian and -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.
Cite
@article{arxiv.2406.06179,
title = {Operator-Valued Twisted Araki-Woods Algebras},
author = {Rahul Kumar R and Melchior Wirth},
journal= {arXiv preprint arXiv:2406.06179},
year = {2024}
}