论文标题

将通用性嵌入ii $ _1 $因素(t)

Embedding universality for II$_1$ factors with property (T)

论文作者

Chifan, Ionut, Drimbe, Daniel, Ioana, Adrian

论文摘要

我们证明,每个可分离的奇特·诺伊曼(Von Neumann)代数都嵌入具有财产(t)的II $ _1 $因子中,可以将其视为具有琐碎的外部自动形态和基本群体。我们还建立了在每个可计数P.M.P.等价关系。这些结果是通过使用最近在\ cite {cios21}中引入的类似花环的产品组获得的。

We prove that every separable tracial von Neumann algebra embeds into a II$_1$ factor with property (T) which can be taken to have trivial outer automorphism and fundamental groups. We also establish an analogous result for the trivial extension over a non-atomic probability space of every countable p.m.p. equivalence relation. These results are obtained by using the class of wreath-like product groups introduced recently in \cite{CIOS21}.

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