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C*-diagonals with Cantor spectrum in Cuntz algebras
Published 27 Jun 2025 in math.OA | (2506.22163v1)
Abstract: We prove that there exists a C*-diagonal with Cantor spectrum in the Cuntz algebra $\mathcal{O}_k$ for $2 \le k < \infty$. Our method generalises to an uncountable family of UCT Kirchberg algebras with distinct K-theory. Moreover, we construct principal \'etale groupoid models for these Cuntz algebras and UCT Kirchberg algebras.
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