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arXiv · 1208.5642

A generalization of expander graphs and local reflexivity of uniform Roe algebras

Hiroki Sako
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Abstract

We introduce a generalization of expander graphs, which is called a weak expander sequence. It is proved that a uniform Roe algebra of a weak expander sequence is not locally reflexive. It follows that uniform Roe algebras of expander graphs are not exact. We introduce the notion of a generalized box space to discuss box spaces and expander sequences in a unified framework. Key tools for the proof are amenable traces and measured groupoids associated to generalized box spaces.

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BibTeXRIS

Hiroki Sako. 2012-08-28. A generalization of expander graphs and local reflexivity of uniform Roe algebras. https://doi.org/10.1016/j.jfa.2013.05.034

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