STABLE RANK FOR INCLUSIONS OF C*-ALGEBRAS

Abstract

When a unital C*-algebra A has topological stable rank one (write tsr (A) = 1), we know that tsr (pAp) = 1 for a non-zero projection p ∈ A. When, however, tsr (A) ≥ 2, it is generally false. We prove that if a unital C*-algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and supp ∈ P(D)tsr (pAp) < ∞, then tsr (A) ≤ 2. As an application let A be a simple unital C*-algebra with tsr (A) = 1 and Property (SP), [Formula: see text] finite groups, αkactions from Gkto Aut ((⋯((A × α1G1) ×α2G2)⋯) ×αk-1Gk-1). (G0= {1}). Then [Formula: see text]