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

Czechoslovak Mathematical Journal

Liu¹  Junping ² 

[1] (corresponding author), School of Mathematical Sciences, Ocean University of China, 238 Songling Road, Qingdao, Shandong, 266100, China;Department of Mathematics, East China Normal University, No. 500, Dongchuan Road, Shanghai, 200041, China

关键词: $AF$-algebra;    extension;    purely infinite simple algebra;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown