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 K 1 -groups up to isomorphism.