论文标题
阶乘相对通勤者和II $ _1 $因素的广义荣格物业
Factorial relative commutants and the generalized Jung property for II$_1$ factors
论文作者
论文摘要
我们介绍了广义的荣格因子的概念：a II $ _1 $ $ m $ $ m $ $ m $的任何两个嵌入在其超能$ m^{\ mathcal u} $中是按$ m^{\ Mathcal u} $的自动形态的。我们表明，$ \ Mathcal r $不是唯一的概括性荣格因子，而是唯一的$ \ Mathcal r^{\ Mathcal U} $ - 可嵌入的概括性Jung Factor。我们使用模型理论技术来获得这些结果。与所使用的技术不可或缺的结果是，如果$ m $基本等同于$ \ Mathcal r $，那么$ m $的任何基本嵌入$ \ \ \ \ \ mathcal r^{\ mathcal u} $都有循序分式相对的交换剂。这回答了一个长期存在的Popa问题，即一个无数$ _1 $因素的家庭。我们还提供了有关超级麦克粉丝概念的新示例和结果，这是II $ _1 $因素的McDuff属性的加强。
We introduce the notion of a generalized Jung factor: a II$_1$ factor $M$ for which any two embeddings of $M$ into its ultrapower $M^{\mathcal U}$ are equivalent by an automorphism of $M^{\mathcal U}$. We show that $\mathcal R$ is not the unique generalized Jung factor but is the unique $\mathcal R^{\mathcal U}$-embeddable generalized Jung factor. We use model-theoretic techniques to obtain these results. Integral to the techniques used is the result that if $M$ is elementarily equivalent to $\mathcal R$, then any elementary embedding of $M$ into $\mathcal R^{\mathcal U}$ has factorial relative commutant. This answers a long-standing question of Popa for an uncountable family of II$_1$ factors. We also provide new examples and results about the notion of super McDuffness, which is a strengthening of the McDuff property for II$_1$ factors.
