Z-stability and finite-dimensional tracial boundaries

Author: 

Toms, A
White, S
Winter, W

Publication Date: 

2015

Journal: 

International Mathematics Research Notices. IMRN

Last Updated: 

2020-03-29T16:23:10.02+01:00

Issue: 

10

DOI: 

10.1093/imrn/rnu001

page: 

2702-2727

abstract: 

We show that a simple separable unital nuclear nonelementary $C^*$-algebra
whose tracial state space has a compact extreme boundary with finite covering
dimension admits uniformly tracially large order zero maps from matrix algebras
into its central sequence algebra. As a consequence, strict comparison implies
$\Z$-stability for these algebras.

Symplectic id: 

1049974

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article