Uniformly super McDuff II1 factors

被引：0

作者：

Goldbring, Isaac ^{[1
]}

Jekel, David ^{[2
]}

Elayavalli, Srivatsav Kunnawalkam ^{[3
]}

Pi, Jennifer ^{[4
]}

机构：

[1] Univ Calif Irvine, Dept Math, 410 Rowland Hall Bldg 400, Irvine, CA 92697 USA

[2] Univ Calif San Diego, Dept Math, 9500 Gilman Dr, La Jolla, CA 92093 USA

[3] UCLA, Inst Pure & Appl Math, 460 Portola Plaza, Los Angeles, CA 90095 USA

[4] Univ Calif Irvine, Dept Math, 340 Rowland Hall Bldg 400, Irvine, CA 92697 USA

来源：

MATHEMATISCHE ANNALEN | 2025年 / 391卷 / 02期

基金：

美国国家科学基金会;

关键词：

MODEL-THEORY; ALGEBRAS; CLASSIFICATION; EQUIVALENCE; AMENABILITY; EMBEDDINGS;

D O I：

10.1007/s00208-024-02959-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce and study the family of uniformly super McDuff II1 factors. This family is shown to be closed under elementary equivalence and also coincides with the family of II1 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 II1 Factors with Property (T). arXiv preprint, 2022). We also show that Popa's family of strongly McDuff II1 factors are uniformly super McDuff. Lastly, we investigate when finitely generic II1 factors are uniformly super McDuff.

引用

页码：2757 / 2781

页数：25

共 36 条

[1]

Atkinson S., 2022, ADV MATH, V396, DOI [10.1016/j.aim.2021.108107, DOI 10.1016/J.AIM.2021.108107]

[2] On Ultraproduct Embeddings and Amenability for Tracial von Neumann Algebras [J].

Atkinson, Scott ;

Elayavalli, Srivatsav Kunnawalkam .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021, 2021 (04) :2882-2918

[3] II1 FACTORS WITH NONISOMORPHIC ULTRAPOWERS [J].

Boutonnet, Remi ;

Chifan, Ionut ;

Ioana, Adrian .

DUKE MATHEMATICAL JOURNAL, 2017, 166 (11) :2023-2051

[4] Topological dynamical systems associated to II1-factors [J].

Brown, Nathanial P. .

ADVANCES IN MATHEMATICS, 2011, 227 (04) :1665-1699

[5]

Chang CC., 2013, MODEL THEORY

[6]

Chifan I., 2022, ARXIV, DOI DOI 10.48550/ARXIV.2205.07442

[7]

Chifan I, 2023, GEOM FUNCT ANAL, V33, P1243, DOI 10.1007/s00039-023-00649-4

[8] PROPERTY-T FOR VONNEUMANN-ALGEBRAS [J].

CONNES, A ;

JONES, V .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1985, 17 (JAN) :57-62

[9] CLASSIFICATION OF INJECTIVE FACTORS - CASES II1, II INFINITY, III LAMBDA, LAMBDA NOT-EQUAL-TO 1 [J].

CONNES, A .

ANNALS OF MATHEMATICS, 1976, 104 (01) :73-115

[10] 2 NEW TYPE-2(I) FACTORS [J].

DIXMIER, J ;

LANCE, EC .

INVENTIONES MATHEMATICAE, 1969, 7 (03) :226-&

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