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Unital extensions of AF-algebras by purely infinite simple algebras

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, No. 500, Dongchuan Road, Shanghai, 200041, China

    Junping Liu

  2. School of Mathematical Sciences, Ocean University of China, 238 Songling Road, Qingdao, Shandong, 266100, China

    Changguo Wei

Authors
  1. Junping Liu
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  2. Changguo Wei
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Corresponding author

Correspondence to Changguo Wei.

Additional information

This work was supported by Shandong Provincial Natural Science Foundations (Grant No. ZR2011AM003 and BS2012SF031) and National Natural Science Foundations of China (Grant No. 11171315 and 11271224). It was also supported by the Research Center for Operator Algebras at ECNU.

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Liu, J., Wei, C. Unital extensions of AF-algebras by purely infinite simple algebras. Czech Math J 64, 989–1001 (2014). https://doi.org/10.1007/s10587-014-0148-z

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  • DOI: https://doi.org/10.1007/s10587-014-0148-z

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