Classification of certain infinite simple \(C^*\)-algebras. II
The follow-up of a paper (with the same title) by the second named author [J. Funct. Anal. 131, No. 2, 415-458 (1995; Zbl 0831.46063)], the construction of classifiable models of separable, purely infinite, simple \(C^*\)-algebras is completed. Algebras in this class of classifiable models are completely determined (up to isomorphism) by the triple \((K_0{\mathcal A}),[1],K_1({\mathcal A})\)) for \(\mathcal A\) unital and by the \(K\)-groups alone for \(\mathcal A\) non-unital. The author gives a necessary and sufficient condition for a \(C^*\)-algebra \(\mathcal A\) to have a model \(C^*\)-algebra \({\mathcal A}_0\) in this class with the same triple (or the same \(K\)-groups in the non-unital case). Moreover, any triple \((G_0,g_0,G_1)\) with \(G_0\), \(G_1\) countable Abelian groups, \(g_0\in G_0\), can be realized in this way; the condition that \(G_1\) has to be torsionfree could now be removed.
classifiable models of separable, purely infinite, simple \(C^*\)-algebras
scientific article; zbMATH DE number 852030