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arXiv · 2203.06366

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

Panchugopal Bikram·Kunal Mukherjee·Éric Ricard·Simeng Wang
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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 $dim(\mathcal{H}_\mathbb{R})\geq 3$. 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.

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Panchugopal Bikram, Kunal Mukherjee, Éric Ricard, Simeng Wang. 2022-03-12. On the factoriality of q-deformed Araki-Woods von Neumann algebras. https://doi.org/10.1007/s00220-022-04535-2

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