Classifiability of crossed products by nonamenable groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-10 DOI:10.1515/crelle-2023-0012

Eusebio Gardella, S. Geffen, J. Kranz, P. Naryshkin

引用次数: 9

Abstract

Abstract We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable Baumslag–Solitar groups, a large class of amalgamated free products, lattices in many Lie groups, A ~ 2 {\widetilde{A}_{2}} -groups, as well as direct products of the above with arbitrary countable groups. As a consequence, crossed products by amenable, minimal and topologically free actions of such groups on compact metric spaces are Kirchberg algebras in the UCT class, and are therefore classified by K-theory.

查看原文本刊更多论文

不可服从群的交叉产物的可分类性

摘要证明了紧度量空间上一大类不可调可数群的所有可调极小作用都具有动态比较。这类包括所有不可调节的双曲群，许多hnn -扩展，不可调节的Baumslag-Solitar群，一大类合并自由积，许多李群中的格，a ~ 2 {\wide}_{2}}群，以及以上与任意可数群的直接积。因此，这些群在紧度量空间上的可服从的、极小的和拓扑自由的交叉积是UCT类中的Kirchberg代数，因此可以用k理论分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.