论文标题
常规夹杂物的结构。 ii：彩坦信封，伪期望和曲折
Structure for Regular Inclusions. II: Cartan envelopes, pseudo-expectations and twists
论文作者
论文摘要
我们介绍了定期包含的cartan包络的概念（c，d）。当存在纸箱信封时，它是独特的，最小的cartan对（c，d）定期嵌入其中。当且仅当（c，d）具有独特的忠实伪预测属性并使用理想的交叉点属性的特征中，我们才证明存在cartan封信。 对于任何覆盖包含，我们都使用适当的线性函数构建了Hausdorff扭曲的类固醇，并用一个扭曲的曲折描述了（C，d）的cartan信封，其单位空间是使用独特的伪宣传构建的C上的一组状态。对于常规的MASA包含，这种扭曲与Weyl Twist不同。在这种情况下，我们表明Weyl Tisws是Hausdorff的，而C恰好存在C对D的有条件期望。 我们表明，定期包含独特的伪预测属性是涵盖包容性，并给出了独特的伪指标属性的其他后果。
We introduce the notion of a Cartan envelope for a regular inclusion (C,D). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,D) regularly embeds. We prove a Cartan envelope exists if and only if (C,D) has the unique faithful pseudo-expectation property and also give a characterization of the Cartan envelope using the ideal intersection property. For any covering inclusion, we construct a Hausdorff twisted groupoid using appropriate linear functionals and we give a description of the Cartan envelope for (C,D) in terms of a twist whose unit space is a set of states on C constructed using the unique pseudo-expectation. For a regular MASA inclusion, this twist differs from the Weyl twist; in this setting, we show that the Weyl twist is Hausdorff precisely when there exists a conditional expectation of C onto D. We show that a regular inclusion with the unique pseudo-expectation property is a covering inclusion and give other consequences of the unique pseudo-expectation property.
