统一超麦克杜夫 $$\hbox {II}_1$$ 因子

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-09-12 DOI:10.1007/s00208-024-02959-w

Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, Jennifer Pi

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引用次数: 0

摘要

我们介绍并研究了均匀超麦克杜夫（\hbox {II}_1\）因子族。这个族被证明在基本等价下是封闭的，并且与阿特金森等人（Adv. Math. 396, 108107, 2022）中介绍的具有布朗性质的 $\hbox {II}_1$ 因子的族重合。我们证明了存在封闭因子的某个族，即所谓的无限泛函因子，是均匀超麦克达夫的，从而改进了奇凡等人最近的一个结果（Embedding Universality for $\hbox {II}_1$ Factors with Property (T). arXiv preprint, 2022）。我们还证明了 Popa 的强 McDuff （\hbox {II}_1\）因子族是均匀超 McDuff 的。最后，我们研究了有限泛函（\hbox {II}_1\）因子是均匀超级麦克达夫的情况。

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Uniformly super McDuff $$\hbox {II}_1$$ factors

We introduce and study the family of uniformly super McDuff $\hbox {II}_1$ factors. This family is shown to be closed under elementary equivalence and also coincides with the family of $\hbox {II}_1$ factors with the Brown property introduced in Atkinson et al. (Adv. Math. 396, 108107, 2022). We show that a certain family of existentially closed factors, the so-called infinitely generic factors, are uniformly super McDuff, thereby improving a recent result of Chifan et al. (Embedding Universality for $\hbox {II}_1$ Factors with Property (T). arXiv preprint, 2022). We also show that Popa’s family of strongly McDuff $\hbox {II}_1$ factors are uniformly super McDuff. Lastly, we investigate when finitely generic $\hbox {II}_1$ factors are uniformly super McDuff.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.