Unital extensions of AF-algebras by purely infinite simple algebras

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 K1-groups up to isomorphism.