C*-diagonals with Cantor spectrum in Cuntz algebras

TL;DR

This paper constructs C*-diagonals with Cantor spectrum in Cuntz algebras and extends the method to a broad class of Kirchberg algebras, providing new models via groupoids.

Contribution

It introduces a method to realize C*-diagonals with Cantor spectrum in Cuntz algebras and extends this to an uncountable family of Kirchberg algebras with distinct K-theory.

Findings

Existence of C*-diagonals with Cantor spectrum in Cuntz algebras.

Construction of principal étale groupoid models for these algebras.

Extension of the method to uncountable families of UCT Kirchberg algebras.

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.