Amenability of coarse spaces and K -algebras.

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-01-01 Epub Date: 2017-11-09 DOI:10.1007/s13373-017-0109-6

Pere Ara, Kang Li, Fernando Lledó, Jianchao Wu

引用次数: 9

Abstract

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. We apply our general analysis to two important classes of algebras: the unital Leavitt path algebras and the translation algebras on locally finite extended metric spaces. In particular, we show that the amenability of a metric space is equivalent to the algebraic amenability of the corresponding translation algebra.

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粗糙空间与K -代数的可调和性。

本文从代数的角度分析了可顺从性和悖论分解的概念。我们考虑了局部有限扩展度量空间和域上一般代数的这种二分法。在代数的范围内，我们还研究了适性与固有无穷的关系。我们将一般分析应用于两类重要的代数:局部有限扩展度量空间上的一元莱维特路径代数和平移代数。特别地，我们证明了度量空间的易受性等价于相应平移代数的代数易受性。

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

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.