Non-isomorphism of A∗n,2≤n≤∞, for a non-separable abelian von Neumann algebra A

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2024-02-14 DOI:10.1007/s00039-024-00669-8

Rémi Boutonnet, Daniel Drimbe, Adrian Ioana, Sorin Popa

引用次数: 0

Abstract

We prove that if A is a non-separable abelian tracial von Neuman algebra then its free powers A^∗n,2≤n≤∞, are mutually non-isomorphic and with trivial fundamental group, \(\mathcal{F}(A^{*n})=1\), whenever 2≤n<∞. This settles the non-separable version of the free group factor problem.

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A∗n,2≤n≤∞ 的非同构性，适用于不可分离的无边际冯-诺依曼代数 A

我们证明，如果 A 是一个不可分离的非等边三叉冯-纽曼代数，那么当 2≤n<∞ 时，它的自由幂 A∗n,2≤n≤∞，是互不同构的，并且具有微不足道的基群，即 \(\mathcal{F}(A^{*n})=1\)。这就解决了自由基因数问题的不可分版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.