2024/06/10 by R, Rahul Kumar, Wirth, Melchior
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2406.06179
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.