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Article overview
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Remarks on factoriality and $q$-deformations | | Adam Skalski
; Simeng Wang
; | | Date: |
14 Jul 2016 | | Abstract: | We prove that the mixed $q$-Gaussian algebra $Gamma_{Q}(H_{mathbb{R}})$
associated to a real Hilbert space $H_{mathbb{R}}$ and a real symmetric matrix
$Q=(q_{ij})$ with $sup|q_{ij}|<1$, is a factor as soon as $dim
H_{mathbb{R}}geq2$. We also discuss the factoriality of $q$-deformed
Araki-Woods algebras, in particular showing that the $q$-deformed Araki-Woods
algebra $Gamma_{q}(H_{mathbb{R}},U_{t})$ given by a real Hilbert space
$H_{mathbb{R}}$ and a strongly continuous group $U_{t}$ is a factor when $dim
H_{mathbb{R}}geq2$ and $U_{t}$ admits an invariant eigenvector. | | Source: | arXiv, 1607.4027 | | Services: | Forum | Review | PDF | Favorites | |
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