Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911902670520320 |
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| author | Bönicke, Christian Li, Kang |
| author_facet | Bönicke, Christian Li, Kang |
| contents | 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 $C(X)\rtimes_r D_\infty$ has finite nuclear dimension and is classifiable by its Elliott invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17178 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension Bönicke, Christian Li, Kang Operator Algebras Dynamical Systems 46L05, 22A22 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 $C(X)\rtimes_r D_\infty$ has finite nuclear dimension and is classifiable by its Elliott invariant. |
| title | Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension |
| topic | Operator Algebras Dynamical Systems 46L05, 22A22 |
| url | https://arxiv.org/abs/2309.17178 |