Cartan subalgebras in uniform Roe algebras

Author: 

White, S
Willett, R

Publication Date: 

21 October 2020

Journal: 

Groups, Geometry, and Dynamics

Last Updated: 

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

Issue: 

3

Volume: 

14

DOI: 

10.4171/GGD/570

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

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article