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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)
##### Keywords:
$$AF$$-algebra; extension; purely infinite simple algebra
Full Text:
##### References:
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