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arXiv · 2205.04013

Tracial approximation and ${\cal Z}$-stability

Huaxin Lin
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Abstract

Let $A$ be a unital separable non-elementary amenable simple stably finite C*-algebra such that its tracial state space has a $σ$-compact countable-dimensional extremal boundary. We show that $A$ is ${\cal Z}$-stable if and only if it has strict comparison and stable rank one. We show that this result also holds for non-unital cases (which may not be Morita equivalent to unital ones).

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Huaxin Lin. 2025-10-28. Tracial approximation and ${\cal Z}$-stability. https://arxiv.org/abs/2205.04013

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