AG Mathematische Physik, Melchior Wirth (IST Wien): Operator-Valued Twisted Araki-Woods Algebras

Melchior Wirth (IST Wien)

Operator-Valued Twisted Araki-Woods Algebras

Abstract:
I will introduce the class of operator-valued twisted Araki-Woods algebras, which are second

quantization von Neumann algebras built on certain Hilbert bimodules over a base von Neumann

algebra. When the base algebra is the field of complex numbers, this class includes the q-Gaussian

algebras and free Araki-Woods factors, and for arbitrary base algebras Shlyakhtenko’s von Neumann

algebras generated by operator-valued semicircular variables fall into this class. In the case when the

base algebra is a type I factor, I will present how a disintegration theory for the underlying Hilbert

bimodules leads to a decomposition as a tensor product of the base algebra and a scalar-valued

twisted Araki-Woods algebra. Moreover, operator-valued twisted Araki-Woods algebras come with

a natural weight, and I will discuss the associated modular theory as well as some sufficient criteria

for factoriality. This is joint work with Rahul Kumar R.