Ara Pere, Li Kang, Lledó Fernando, Wu Jianchao
1Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
2Department of Mathematics, University of Münster, Einsteinstr. 62, 48149 Münster, Germany.
Bull Math Sci. 2018;8(2):257-306. doi: 10.1007/s13373-017-0109-6. Epub 2017 Nov 9.
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.
在本文中，我们从代数角度分析顺从性和悖论分解的概念。我们考虑局部有限扩展度量空间以及域上的一般代数的这种二分法。在代数的背景下，我们还研究顺从性与恰当无限性之间的关系。我们将一般分析应用于两类重要的代数：幺半莱维特路径代数和局部有限扩展度量空间上的平移代数。特别地，我们表明度量空间的顺从性等同于相应平移代数的代数顺从性。
