Proves the existence of C*-diagonals with Cantor spectrum in Cuntz algebras, indicating broader implications for UCT Kirchberg algebras.
We prove that there exists a C ⁎ -diagonal with Cantor spectrum in the Cuntz algebra O k for 2 ≤ k < ∞ . Our method generalises to an uncountable family of UCT Kirchberg algebras with distinct K-theory. Moreover, we construct principal étale groupoid models for these Cuntz algebras and UCT Kirchberg algebras.
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Evington et al. (2026) studied this question.
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