Every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite, with the consequence that minimal crossed products are Z-stable and Elliott-classifiable.
Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-alegbras which satisfy the UCT and have finite rational tracial rank.
representative citing papers
Constructs minimal homeomorphisms on spaces with prescribed K-theory/co-homology and minimal orbit-breaking relations realizing arbitrary countable abelian K-theory pairs via groupoid C*-algebras.
Comparison radius of C(X) ⋊ ℤ^d is ≤ (1/2) mean topological dimension for minimal free ℤ^d-actions, implying classifiability when mean dimension vanishes.
citing papers explorer
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Elementary amenability and almost finiteness
Every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite, with the consequence that minimal crossed products are Z-stable and Elliott-classifiable.
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Constructions in minimal amenable dynamics and applications to the classification of $\mathrm{C}^*$-algebras
Constructs minimal homeomorphisms on spaces with prescribed K-theory/co-homology and minimal orbit-breaking relations realizing arbitrary countable abelian K-theory pairs via groupoid C*-algebras.
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Comparison radius and mean topological dimension: $\mathbb{Z}^d$-actions
Comparison radius of C(X) ⋊ ℤ^d is ≤ (1/2) mean topological dimension for minimal free ℤ^d-actions, implying classifiability when mean dimension vanishes.