多项式增长、比较和小边界性质
Polynomial growth, comparison, and the small boundary property
摘要：
证明了紧致度量化空间上多项式增长的有限生成群的极小作用具有比较性。由此得出，如果这样的作用具有小边界性质，那么它几乎是有限的，并且它的$C^*$交叉积是$\mathcal{Z}$ -稳定的，因此这种交叉积可以用它们的Elliott不变量来分类.
英文摘要：
We show that a minimal action of a finitely generated group of polynomial growth on a compact metrizable space has comparison. It follows that if such an action has the small boundary property then it is almost finite and its $C^*$-crossed product is $\mathcal{Z}$-stable, and consequently that such crossed products are classified by their Elliott invariant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
