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arXiv · 2508.07327

A note on the quasi-local algebra of expander graphs

Bruno M. Braga·Ján Špakula·Alessandro Vignati
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Abstract

We show that the quasi-local algebra of a coarse disjoint union of expander graphs does not contain a Cartan subalgebra isomorphic to $\ell_\infty$. N. Ozawa has recently shown that these algebras are distinct from the uniform Roe algebras of expander graphs, and our result describes a further difference.

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Bruno M. Braga, Ján Špakula, Alessandro Vignati. 2025-08-10. A note on the quasi-local algebra of expander graphs. https://arxiv.org/abs/2508.07327

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