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Unital extensions of A F -algebras by purely infinite simple algebras

Junping Liu;  Changguo Wei — 2014

Czechoslovak Mathematical Journal

In this paper, we consider the classification of unital extensions of A F -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 A F -algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of A F -algebras by stable purely infinite simple C * -algebras with nontrivial...

Pseudometrics on Ext-semigroups

Changguo Wei;  Xiangmei Zhao;  Shudong Liu — 2020

Czechoslovak Mathematical Journal

This paper considers certain pseudometric structures on Ext-semigroups and gives a unified characterization of several topologies on Ext-semigroups. It is demonstrated that these Ext-semigroups are complete topological semigroups. To this end, it is proved that a metric induces a pseudometric on a quotient space with respect to an equivalence relation if it has certain invariance. We give some properties of this pseudometric space and prove that the topology induced by the pseudometric coincides...

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