Nuclear Dimension of Subhomogeneous Twisted Groupoid C∗-algebras and Dynamic Asymptotic Dimension

Bönicke C, Li K (2024)


Publication Type: Journal article

Publication year: 2024

Journal

Book Volume: 2024

Pages Range: 11597-11610

Journal Issue: 16

DOI: 10.1093/imrn/rnae133

Abstract

We characterize 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 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 has finite nuclear dimension and is classifiable by its Elliott invariant.

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APA:

Bönicke, C., & Li, K. (2024). Nuclear Dimension of Subhomogeneous Twisted Groupoid C∗-algebras and Dynamic Asymptotic Dimension. International Mathematics Research Notices, 2024(16), 11597-11610. https://doi.org/10.1093/imrn/rnae133

MLA:

Bönicke, Christian, and Kang Li. "Nuclear Dimension of Subhomogeneous Twisted Groupoid C∗-algebras and Dynamic Asymptotic Dimension." International Mathematics Research Notices 2024.16 (2024): 11597-11610.

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