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arXiv · 2108.08970

Tracial approximate divisibility and stable rank one

Xuanlong Fu·Kang Li·Huaxin Lin
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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.

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Xuanlong Fu, Kang Li, Huaxin Lin. 2021-08-20. Tracial approximate divisibility and stable rank one. https://arxiv.org/abs/2108.08970

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