The Stable Rank of Diagonally Constructed ASH Algebras

2017/09/28 by Lutley, James
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1709.10081

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.

Related

• The Stable Rank of Diagonal ASH Algebras and Crossed Products by Minimal Homeomorphisms
• Permanence of stable rank one for centrally large subalgebras and crossed products by minimal homeomorphisms
• Homotopical Stable Ranks for Certain C*-algebras
• Stable Recursive Subhomogeneous Algebras
• Homotopical Stable Ranks for Certain C^∗-algebras Associated to Groups