Tracial approximate divisibility and stable rank one

Xuanlong Fu; Kang Li; Huaxin Lin

Tracial approximate divisibility and stable rank one

Operator Algebras 2021-09-07 v2

Authors: Xuanlong Fu , Kang Li , Huaxin Lin

Abstract

We show that every separable simple tracially approximately divisible $C^*$ -algebra has strict comparison, is either purely infinite, or has stable rank one. As a consequence, we show that every (non-unital) finite simple ${\cal Z}$ -stable $C^*$ -algebra has stable rank one.

Keywords

c*-algebras cuntz semigroup graph algebras

Cite

@article{arxiv.2108.08970,
  title  = {Tracial approximate divisibility and stable rank one},
  author = {Xuanlong Fu and Kang Li and Huaxin Lin},
  journal= {arXiv preprint arXiv:2108.08970},
  year   = {2021}
}

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