# Operator-Valued Twisted Araki–Woods Algebras

## TL;DR

This paper introduces a new class of operator algebras and explores their properties and isomorphism types.

## Contribution

The paper introduces and analyzes operator-valued twisted Araki–Woods algebras, extending previous algebraic frameworks.

## Key findings

- Operator-valued twisted Araki–Woods algebras generalize q-Gaussian and q-Araki–Woods algebras.
- A disintegration theory reduces their isomorphism type over type II factors to the scalar-valued case.
- The paper characterizes the modular theory of the natural weight and provides criteria for factoriality.

## 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 \documentclass[12pt]{minimal}
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\begin{document}$$\textrm{I}$$\end{document}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.