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# On the Classification of Simple Stably Projectionless $\C^*$-Algebras

It is shown that simple stably projectionless $\C^S*$-algebras which are inductive limits of certain specified building blocks with trivial $\K$-theory are classified by their cone of positive traces with distinguished subset. This is the first example of an isomorphism theorem verifying the conjecture of Elliott for a subclass of the stably projectionless algebras.
 MSC Classifications: 46L35 - Classifications of $C^*$-algebras 46L05 - General theory of $C^*$-algebras