English

Extensions of C*-algebas by a small ideal

Operator Algebras 2020-06-02 v1

Abstract

We classify all essential extensions of the form 0\W\DA00 \rightarrow \W \rightarrow \D \rightarrow A \rightarrow 0 where \W\W is the unique separable simple C*-algebra with a unique tracial state, with finite nuclear dimension and with Ki(\W)={0}K_i(\W)=\{0\} (i=0,1i=0,1) which satisfies the Universal Coefficient theorem (UCT), and AA is a separable amenable \W\W-embeddable C*-algebra which satisfies the UCT. We actually prove more general results. We also classify a class of amenable \CA s which have only one proper closed ideal \W.\W.

Keywords

Cite

@article{arxiv.2006.00132,
  title  = {Extensions of C*-algebas by a small ideal},
  author = {Huaxin Lin and Ping Wong Ng},
  journal= {arXiv preprint arXiv:2006.00132},
  year   = {2020}
}