Unital extensions of $AF$-algebras by purely infinite simple algebras

Liu, Junping ; Wei, Changguo

Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 989-1001

Abstract (VO)

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.

Détail

DOI : 10.1007/s10587-014-0148-z

Classification : 46L05, 46L35
Keywords: $AF$-algebra; extension; purely infinite simple algebra

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