Single generation of transformation group algebras

Abstract

We prove that $C(X)⋊\Gamma$ is singly generated whenever $\Gamma$ 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.

arXiv commentPreliminary version, 19 pages. The work is carried out using ChatGPT