Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension

Abstract

We characterise subhomogeneity for twisted étale groupoid C*-algebras and obtain an upper bound on their nuclear dimension. As an application, we remove the principality assumption in recent results on upper bounds on the nuclear dimension of a twisted étale groupoid C*-algebra in terms of the dynamic asymptotic dimension of the groupoid and the covering dimension of its unit space. As a non-principal example, we show that the dynamic asymptotic dimension of any minimal (not necessarily free) action of the infinite dihedral group $D_{\infty }$ on an infinite compact Hausdorff space $X$ is always one. So if we further assume that $X$ is second-countable and has finite covering dimension, then $C(X){⋊}_r{D}_{\infty }$ has finite nuclear dimension and is classifiable by its Elliott invariant.

16 pages, this version will appear in IMRN

References in corpus (3)

• Alexandrov groupoids and the nuclear dimension of twisted groupoid ${\mathrm{C}}^{\ast }$-algebras
• On the dynamic asymptotic dimension of étale groupoids
• Long thin covers and nuclear dimension

Cited by in corpus (2)

• On the dynamic asymptotic dimension of étale groupoids
• Paper-folding models for the CAR algebra