Author
White, S
Willett, R
Journal title
Groups, Geometry, and Dynamics
DOI
10.4171/GGD/570
Issue
3
Volume
14
Last updated
2022-08-05T20:45:50+01:00
Page
949-989
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.
Symplectic ID
1050048