A generalization of expander graphs and local reflexivity of uniform Roe algebras
Operator Algebras
2015-03-13 v4 Group Theory
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1208.5642,
title = {A generalization of expander graphs and local reflexivity of uniform Roe algebras},
author = {Hiroki Sako},
journal= {arXiv preprint arXiv:1208.5642},
year = {2015}
}
Comments
23 pages, section 2 revised