# Cartan subalgebras in uniform Roe algebras

White, S
Willett, R

21 October 2020

## Journal:

Groups, Geometry, and Dynamics

## Last Updated:

2021-10-11T13:48:10.36+01:00

3

14

10.4171/GGD/570

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.

1050048