具有弱三元罗克林性质的有限群作用交叉积的稳定秩

Xiaochun Fang, Zhongli Wang
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引用次数: 0

摘要

让 $A$ 是一个无限维稳定有限简单单素 C* 代数,让 $G$ 是一个有限群,让 $\alpha\colon G\rightarrow \mathrm{Aut}(A)$ 是 $G$ 在 $A$ 上的作用,它具有弱三维罗克林性质。我们证明,如果 $A$ 具有性质 (TM),那么交叉积 $A\rtimes_\alphaG$ 也具有性质 (TM)。作为推论,如果 $A$ 是一个无限维不可分的简单单素 C* 代数,它具有稳定的秩一,并且严格比较,$alpha/colon G\rightarrow \mathrm{Aut}(A)$ 是无穷群 $G$ 对 $A$ 的作用,具有弱三维罗克林性质,那么 $A\rtimes_\alpha G$ 具有稳定的秩一。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stable rank for crossed products by finite group actions with the weak tracial Rokhlin property
Let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, let $G$ be a finite group, and let $\alpha\colon G\rightarrow \mathrm{Aut}(A)$ be an action of $G$ on $A$ which has the weak tracial Rokhlin property. We prove that if $A$ has property (TM), then the crossed product $A\rtimes_\alpha G$ has property (TM). As a corollary, if $A$ is an infinite-dimensional separable simple unital C*-algebra which has stable rank one and strict comparison, $\alpha\colon G\rightarrow \mathrm{Aut}(A)$ is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin property, then $A\rtimes_\alpha G$ has stable rank one.
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