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Cartan subalgebras in uniform Roe algebras

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arxiv 1808.04410 v2 pith:76V6IOK7 submitted 2018-08-13 math.OA math.DSmath.MG

Stuart White , Rufus Willett This is my paper · ORCID
classification math.OAmath.DSmath.MG
keywords algebrasuniformwhenautomorphismcartaninclusioninsidespace
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abstract

In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion $B\subseteq A$ of $\mathrm{C}^*$-algebras is isomorphic to the canonical inclusion of $\ell^\infty(X)$ inside a uniform Roe algebra $C^*_u(X)$ associated to a metric space of bounded geometry. We obtain uniqueness results for `Roe Cartans' inside uniform Roe algebras up to automorphism when $X$ coarsely embeds into Hilbert space, and up to inner automorphism when $X$ has property A.

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  1. Quasi-local Algebras and Asymptotic Expanders

    math.OA 2019-08 accept novelty 8.0 of 10

    The paper defines asymptotic expanders, characterizes quasi-locality of averaging projections via them, and proves the uniform quasi-local algebra is nuclear iff the space has Property A.

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