On classification of non-unital amenable simple C*-algebras, III, Stably projectionless C*-algebras

TL;DR

This paper proves that two separable simple stably projectionless amenable ${ m Z}$-stable $C^*$-algebras satisfying the UCT are isomorphic if they share the same Elliott invariant, advancing classification theory.

Contribution

It establishes a classification result for a class of stably projectionless amenable ${ m Z}$-stable $C^*$-algebras based on their Elliott invariants.

Findings

Isomorphism characterized by Elliott invariant for the class

Extension of classification results to stably projectionless algebras

Supports the Elliott classification program for broader C*-algebra classes

Abstract

We show, based on previous results, that two separable simple stably projectionless amenable ${\cal Z}$-stable $C^*$-algebras which satisfy the UCT are isomorphic if and only if they have the same Elliott invariant.