On classification of non-unital amenable simple C*-algebras, II

Abstract

We present a classification theorem for separable amenable simple stably projectionless C∗-algebras with finite nuclear dimension whose K0 vanish on traces which satisfy the Universal Coefficient Theorem. One of C∗-algebras in the class is denoted by Z0 which has a unique tracial state, K0(Z0)=Z and K1(Z0)={0}. Let A and B be two separable amenable simple C∗-algebras satisfying the UCT. We show that A⊗Z0≅B⊗Z0 if and only if Ell(A⊗Z0)=Ell(B⊗Z0). A class of simple separable C∗-algebras which are approximately sub-homogeneous whose spectra having bounded dimension is shown to exhaust all possible Elliott invariant for C∗-algebras of the form A⊗Z0, where A is any finite separable simple amenable C∗-algebras.