Polynomial growth, comparison, and the small boundary property

Polynomial growth, comparison, and the small boundary property

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 is free and has the small boundary property then it is almost finite and its C⁎-crossed product is Z-stable, and consequently that such cro...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2022-09, Vol.406, p.108519, Article 108519
1. Verfasser: Naryshkin, Petr
Format: Artikel
Sprache:eng
Schlagworte:
Classification of [formula omitted]-algebras
Comparison
Crossed products
Polynomial growth
Small boundary property
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Zusammenfassung: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 is free and 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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108519