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Keywords:
$AF$-algebra; extension; purely infinite simple algebra
$AF$-algebra; extension; purely infinite simple algebra
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.
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