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

Title:

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

Creator:

Liu, Junping and Wei, Changguo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7b765289-826f-418c-b249-fe28c3da446c
uuid:7b765289-826f-418c-b249-fe28c3da446c

Subject:

$AF$-algebra, extension, and purely infinite simple algebra

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

989-1001

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:4

Harvested from:

CDK

Metadata only:

false