Generator masas in $q$-deformed Araki-Woods von Neumann algebras and factoriality

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

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

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

The $q$-deformed Araki-Woods von Neumann algebras $Γ_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ 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.

通过共轭变量完全解决 $q$-Araki-Woods 冯·诺伊曼代数的因子性问题

Full solution of the factoriality question for $q$-Araki-Woods von Neumann algebras via conjugate variables

利用共轭变量方法及抽象结果，完全证明了一般情形下生成元数至少为二的 $q$-Araki-Woods 冯·诺伊曼代数的因子性，并确立其非内射性、确定因子类型及有限生成时的固体性与完全性。

混合$q$-Araki-Woods代数的共轭变量方法：因子性与非内射性

Conjugate variables approach to mixed $q$-Araki-Woods algebras: Factoriality and non-injectivity

本文利用共轭变量方法，在最一般情形下证明了与可分实Hilbert空间等结构关联的混合$q$-Araki-Woods von Neumann代数的因子性与非内射性。

Remarks on factoriality and $q$-deformations

We prove that the mixed $q$-Gaussian algebra $Γ_{Q}(H_{\mathbb{R}})$ 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 $Γ_{q}(H_{\mathbb{R}},U_{t})$ 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.

自由 Araki-Woods 因子的扩张结构

Structure of extensions of free Araki-Woods factors

本文研究了可数群对自由Araki-Woods因子的Bogoljubov作用产生的交叉积von Neumann代数结构，解决了因子性与Connes型分类问题，给出了丰满性与强坚固性准则，并构造出具有特定性质的III型因子新例子。