The Ordered K-theory of a Full Extension

Abstract

AbstractLet be a C*-algebra with real rank zero that has the stable weak cancellation property. Let be an ideal of such that is stable and satisfies the corona factorization property. We prove thatis a full extension if and only if the extension is stenotic and K-lexicographic. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West, and the first named author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*- algebra.