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

We present a classification theorem for separable amenable simple stably projectionless C*-algebras with finite nuclear dimension whose K-0 vanish on traces which satisfy the Universal Coefficient Theorem. One of C*-algebras in the class is denoted by Z(0) which has a unique tracial state, K-0(Z(0)) = Z and K-1(Z(0)) = {0}. Let A and B be two separable amenable simple C*-algebras satisfying the UCT. We show that A circle times Z(0) congruent to B circle times Z(0) if and only if Ell(A circle times Z(0)) = Ell(B circle times Z(0)). 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 circle times Z(0), where A is any finite separable simple amenable C*-algebras. (C) 2020 Elsevier B.V. All rights reserved.