论文标题
关于Popa的阶乘通勤嵌入问题
On Popa's factorial commutant embedding problem
论文作者
论文摘要
Sorin Popa的一个开放问题询问是否每个$ r^{\ Mathcal {u}} $ - 可嵌入的因子将嵌入到$ r^{\ mathcal {u}} $中，并带有fastorial相对交换剂。我们表明，有一个本地通用的McDuff II $ _1 $ $ m $ $ M $，以便每个属性（T）因子将嵌入到$ m^{\ Mathcal {u}} $中，并带有阶乘相对通勤。我们还讨论了如何使用我们的策略来解决POPA的财产问题（T）因素，如果操作员代数模型中的某个开放问题具有积极的解决方案。
An open question of Sorin Popa asks whether or not every $R^{\mathcal{U}}$-embeddable factor admits an embedding into $R^{\mathcal{U}}$ with factorial relative commutant. We show that there is a locally universal McDuff II$_1$ factor $M$ such that every property (T) factor admits an embedding into $M^{\mathcal{U}}$ with factorial relative commutant. We also discuss how our strategy could be used to settle Popa's question for property (T) factors if a certain open question in the model theory of operator algebras has a positive solution.
