论文标题
几乎有限，比较和曲折$ \ Mathcal {z} $ - 稳定性
Almost finiteness, comparison, and tracial $\mathcal{Z}$-stability
论文作者
论文摘要
受Kerr在拓扑动力学上的工作的启发，我们定义了Tracial $ \ Mathcal {Z} $ - sub- $ c^*$ - 代数的稳定性。我们证明，对于可数的离散$ g $，在紧凑的Metrizable Space $ x $，Tracial $ \ Mathcal {Z} $上的可自由和最低限度地作用 - sub- $ c^*$ - algebra $（c（x）\ subseteq c（x）\ rtimes g）的稳定性。因此，Tracial $ \ Mathcal {Z} $ - 稳定性等于几乎有限的动作，只要动作具有小边界属性即可。
Inspired by Kerr's work on topological dynamics, we define tracial $\mathcal{Z}$-stability for sub-$C^*$-algebras. We prove that for a countable discrete amenable group $G$ acting freely and minimally on a compact metrizable space $X$, tracial $\mathcal{Z}$-stability for the sub-$C^*$-algebra $(C(X)\subseteq C(X)\rtimes G)$ implies that the action has dynamical comparison. Consequently, tracial $\mathcal{Z}$-stability is equivalent to almost finiteness of the action, provided that the action has the small boundary property.
