On the factoriality of q-deformed Araki-Woods von Neumann algebras

Abstract

The $q$-deformed Araki-Woods von Neumann algebras ${\Gamma }_q({\mathcal{H}}_{\mathbb{R}},U_t{)}^{\prime \prime }$ are factors for all $q\in (-1,1)$ whenever $dim({\mathcal{H}}_{\mathbb{R}})\ge 3$. When $dim({\mathcal{H}}_{\mathbb{R}})=2$ they are factors as well for all $q$ so long as the parameter defining $(U_t)$ is `small' or $1$ $($trivial$)$ as the case may be.

25 pages

References in corpus (8)

• $q$-Gaussian processes: non-commutative and classical aspects
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Cited by in corpus (3)

• Full solution of the factoriality question for $q$-Araki-Woods von Neumann algebras via conjugate variables
• Conjugate variables approach to mixed $q$-Araki-Woods algebras: Factoriality and non-injectivity
• Singularity of the generator subalgebra in mixed $q$-Gaussian algebras