The Stable Rank of Diagonally Constructed ASH Algebras

TL;DR

This paper introduces diagonal subhomogeneous algebras and proves that their simple limits, including crossed products from minimal homeomorphisms, have stable rank one, advancing understanding of their structure.

Contribution

It defines diagonal subhomogeneous algebras, introduces diagonal maps, and proves that their simple limits have stable rank one, including applications to crossed products.

Findings

Simple limits of diagonal subhomogeneous algebras have stable rank one

Crossed products from minimal homeomorphisms have stable rank one

Provides a new class of algebras with stable rank one

Abstract

We introduce a class of recursive subhomogeneous algebras that we call diagonal subhomogeneous and we give a notion of diagonal maps between these algebras. We show that any simple limit of diagonal subhomogeneous algebras with diagonal maps has stable rank one. As an application we show that for any minimal homeomorphism of a compact Hausdorff space the associated crossed product has stable rank one.