Geodesic
Unital extensions of $AF$-algebras by purely infinite simple algebras
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 989-1001.

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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.
DOI : 10.1007/s10587-014-0148-z
Classification : 46L05, 46L35
Keywords: $AF$-algebra; extension; purely infinite simple algebra 
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Liu, Junping; Wei, Changguo. Unital extensions of $AF$-algebras by purely infinite simple algebras. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 989-1001. doi : 10.1007/s10587-014-0148-z. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0148-z/

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