Tracial oscillation zero and Z-stability
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916098435186688 |
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| author | Lin, Huaxin |
| author_facet | Lin, Huaxin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12036 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Tracial oscillation zero and Z-stability Lin, Huaxin Operator Algebras 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. |
| title | Tracial oscillation zero and Z-stability |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2112.12036 |