We classify all essential extensions of the form

$$
0 \rightarrow \mathcal{B} \rightarrow \mathcal{D} \rightarrow C(X) \rightarrow 0
$$

where $\mathcal{B}$ is a nonunital, simple, separable, finite, real rank zero, $\mathcal{Z}$\-stable $C^*$\-algebra with continuous scale, and where $X$ is a finite CW complex. In fact, we prove that there is a group isomorphism

$$
\mathbf{Ext}(C(X), \mathcal{B}) \rightarrow KK(C(X), \mathcal{M}(\mathcal{B})/\mathcal{B}).
$$

Purely infinite corona algebras and extensions

Ping Wong Ng

Abstract

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