Single generation of transformation group algebras

Abstract

We prove that $C(X)\rtimesΓ$ is singly generated whenever $Γ$ is a finitely generated discrete amenable group and its action on the nonempty compact metrizable space $X$ is free, minimal, and has the uniform Rokhlin property and Cuntz comparison of open sets. In particular, every free minimal $\mathbb Z^d$-crossed product with metrizable underlying space is singly generated.