Principal Groupoid Models for Cuntz Algebras and their Dynamic Asymptotic Dimension
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909938336399360 |
|---|---|
| author | Evington, Samuel Sibbel, Philipp |
| author_facet | Evington, Samuel Sibbel, Philipp |
| contents | We compute the dynamic asymptotic dimension of the principal groupoid models for the Cuntz algebras $\mathcal{O}_k$ for $2 \leq k < \infty$ that have arisen from work of Winter and the authors. Our method generalises to a wide class of Deaconu-Renault groupoids. As an application of our results, we prove that $\mathcal{O}_2$ has infinitely many non-conjugate C$^*$-diagonals with Cantor spectrum, and we generalise this result to other Cuntz algebras by combining the main result with work of Kopsacheilis-Winter and Brown-Clark-Sierakowski-Sims. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principal Groupoid Models for Cuntz Algebras and their Dynamic Asymptotic Dimension Evington, Samuel Sibbel, Philipp Operator Algebras 46L05, 46L35, 22A22 We compute the dynamic asymptotic dimension of the principal groupoid models for the Cuntz algebras $\mathcal{O}_k$ for $2 \leq k < \infty$ that have arisen from work of Winter and the authors. Our method generalises to a wide class of Deaconu-Renault groupoids. As an application of our results, we prove that $\mathcal{O}_2$ has infinitely many non-conjugate C$^*$-diagonals with Cantor spectrum, and we generalise this result to other Cuntz algebras by combining the main result with work of Kopsacheilis-Winter and Brown-Clark-Sierakowski-Sims. |
| title | Principal Groupoid Models for Cuntz Algebras and their Dynamic Asymptotic Dimension |
| topic | Operator Algebras 46L05, 46L35, 22A22 |
| url | https://arxiv.org/abs/2512.01812 |