# Factoriality of $q$-deformed Araki-Woods von Neumann algebras

## TL;DR

This paper proves that $q$-deformed Araki-Woods von Neumann algebras are factors when the real Hilbert space dimension is at least three, extending understanding of their structural properties.

## Contribution

It establishes the factoriality of $q$-Araki-Woods von Neumann algebras for a broad class of parameters and dimensions, advancing the theory of deformed operator algebras.

## Key findings

- $q$-Araki-Woods algebras are factors for $dim( ext{real Hilbert space}) extgreater= 3$
- The result holds for all $q$ in $(-1,1)$
- Provides new insights into the structure of deformed von Neumann algebras

## Abstract

It is proved that the $q$-Araki-Woods von Neumann algebras $\Gamma_q(\CH_\R,U_t)^{\prime\prime}$ for $q\in (-1,1)$ are factors if $dim(\CH_\R)\geq 3$.

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Source: https://tomesphere.com/paper/1703.04924