Classification of a family of non-almost-periodic free Araki–Woods factors
Classification of a family of non-almost-periodic free Araki–Woods factors
复制标题
非几乎周期性自由 Araki-Woods 因子族的分类
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Vaes
中科院分区：
文献类型：
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作者：
Cyril Houdayer;D. Shlyakhtenko;S. Vaes
我们得到了一大类非概周期自由Araki-Woods因子$Gamma（mu,m）”$达到同构的完全分类。我们通过证明自由Araki-Woods因子$Gamma(mu, m)"$产生于$mathbf{R}$上的有限对称Borel测度$mu$，其原子部分$mu_a$是非零且不集中于${0}$，其联合测度类$mathcal C（igvee_{k geq 1} mu^{ast k}）$为不变量来实现这一点。我们的关键技术成果是两个忠实法向状态的统一共轭的变形/刚度判据。我们也用它来推导出自由积冯诺依曼代数的刚性定理和分类定理。
We obtain a complete classification of a large class of non almost periodic free Araki-Woods factors $Gamma(mu,m)"$ up to isomorphism. We do this by showing that free Araki-Woods factors $Gamma(mu, m)"$ arising from finite symmetric Borel measures $mu$ on $mathbf{R}$ whose atomic part $mu_a$ is nonzero and not concentrated on ${0}$ have the joint measure class $mathcal C(igvee_{k geq 1} mu^{ast k})$ as an invariant. Our key technical result is a deformation/rigidity criterion for the unitary conjugacy of two faithful normal states. We use this to also deduce rigidity and classification theorems for free product von Neumann algebras.