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.

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 $dim(\CH_\R)\geq 3$.