A class of simple C*-algebras with stable rank one

TL;DR

This paper characterizes a class of simple, unital C*-algebras constructed as inductive limits of matrix algebras over compact spaces with diagonal connecting maps, proving they have stable rank one without dimension growth assumptions.

Contribution

It provides a new simplicity characterization and proves stable rank one for these algebras, broadening understanding of their structure without dimension growth constraints.

Findings

Algebras are simple and unital under the new characterization.

Such algebras have stable rank one.

Results hold without dimension growth assumptions.

Abstract

We study the limits of inductive sequences (A_i,\phi_i) where each A_i is a direct sum of full matrix algebras over compact metric spaces and each partial map of \phi_i is diagonal. We give a new characterisation of simplicity for such algebras, and apply it to prove that the said algebras have stable rank one whenever they are simple and unital. Significantly, our results do not require any dimension growth assumption.