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arXiv · 2112.12036

Tracial oscillation zero and Z-stability

Huaxin Lin
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Abstract

Let $A$ be a (not necessarily unital) separable non-elementary simple amenable C*-algebra whose tracial basis may not have finite covering dimension and may not be compact but satisfies certain condition (C). We show that $A$ is ${\cal Z}$-stable if and only if $A$ has strict comparison for positive elements. Extremal boundaries of simplexes which satisfy condition (C) may contain countable disjoint unions of $n$-dimensional cubes ($n\in \N$) as a subset.

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Huaxin Lin. 2021-12-22. Tracial oscillation zero and Z-stability. https://arxiv.org/abs/2112.12036

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