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

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

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.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Newcastle University GB United Kingdom (GB)

How to cite

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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