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Unital extensions of \(AF\)-algebras by purely infinite simple algebras. (English) Zbl 1349.46068
Summary: In this paper, we consider the classification of unital extensions of \(AF\)-algebras by their six-term exact sequences in \(K\)-theory. Using the classification theory of \(C^*\)-algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of \(AF\)-algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of \(AF\)-algebras by stable purely infinite simple \(C^*\)-algebras with nontrivial \(K_1\)-groups up to isomorphism.
MSC:
46L35 Classifications of \(C^*\)-algebras
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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