1. Unital extensions of $AF$-algebras by purely infinite simple algebras
- Creator:
- Liu, Junping and Wei, Changguo
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- $AF$-algebra, extension, and purely infinite simple algebra
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public