Amenability of coarse spaces and -algebras.

Authors:
Kang Li
Kang Li
Harbin Medical University
China

Bull Math Sci 2018 9;8(2):257-306. Epub 2017 Nov 9.

5Department of Mathematics, Penn State University, 109 McAllister Building, University Park, PA 16802 USA.

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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http://link.springer.com/10.1007/s13373-017-0109-6
Publisher Site
http://dx.doi.org/10.1007/s13373-017-0109-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6434994PMC
November 2017
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