Mean dimension and a non-embeddable example for amenable group actions

Abstract

For every infinite (countable discrete) amenable group $G$ and every positive integer $d$ we construct a minimal $G$-action of mean dimension $d/2$ which cannot be embedded in the full $G$-shift on $([0,1{]}^d{)}^G$.

21 pages. To be published in Fundamenta Mathematicae