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arXiv · 2512.01812

Principal Groupoid Models for Cuntz Algebras and their Dynamic Asymptotic Dimension

Samuel Evington·Philipp Sibbel
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Abstract

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.

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Samuel Evington, Philipp Sibbel. 2025-12-01. Principal Groupoid Models for Cuntz Algebras and their Dynamic Asymptotic Dimension. https://arxiv.org/abs/2512.01812

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