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arXiv · 1908.07814

Quasi-local Algebras and Asymptotic Expanders

Kang Li·Piotr Nowak·Ján Špakula·Jiawen Zhang
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Abstract

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some $C^*$-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.

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BibTeXRIS

Kang Li, Piotr Nowak, Ján Špakula, Jiawen Zhang. 2019-08-21. Quasi-local Algebras and Asymptotic Expanders. https://arxiv.org/abs/1908.07814

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