A direct proof of Z-stability for AH algebras of bounded topological dimension

TL;DR

This paper provides a direct proof that certain AH C*-algebras with bounded topological dimension are Z-stable, extending to cases with exponential dimension growth, without relying on classification theory.

Contribution

It offers a new, direct proof of Z-stability for AH algebras with bounded or exponential dimension growth, bypassing the need for classification theory.

Findings

AH algebras with no dimension growth are Z-stable

The proof applies to algebras with exponential dimension growth

Z-stability is established without classification theory

Abstract

We prove that a unital simple approximately homogeneous (AH) C*-algebra with no dimension growth absorbs the Jiang-Su algebra tensorially without appealing to the classification theory of these algebras. Our main result continues to hold under the slightly weaker hypothesis of exponentially slow dimension growth.