Tracial approximate divisibility and stable rank one
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.08970
- arXiv:
- arXiv:2108.08970
- Bibcode:
- 2021arXiv210808970F
- Keywords:
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- Mathematics - Operator Algebras;
- 46L35;
- 46L05
- E-Print:
- This is a revision