A class of simple [formula omitted]-algebras with stable rank one

Abstract

We study the limits of inductive sequences ( A i , ϕ i ) where each A i is a direct sum of full matrix algebras over compact metric spaces and each partial map of ϕ 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.