Polynomial growth, comparison, and the small boundary property

2021/08/10 by Petr Naryshkin, Naryshkin, Petr
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2108.04670

openalex publication_date 2021/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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 Z-stable, and consequently that such crossed products are classified by their Elliott invariant.

Related

• Invariant ergodic measures and the classification of crossed product C^∗-algebras
• The small boundary property in products
• Essential freeness, allostery and Z-stability of crossed products
• Almost finiteness, comparison, and tracial Z-stability
• Elementary amenability and almost finiteness