Separable space

Philosophy

Pure mathematics

Mathematical physics

Discrete mathematics

Dimension (graph theory)

Computer science

Simple (philosophy)

Bounded function

Homogeneous

Unital

Mathematics

Invariant (physics)

Epistemology

Mathematical analysis

Artificial intelligence

Combinatorics

Class (philosophy)

Algebra over a field

Journal of Geometry and Physics

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.

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