C*-diagonals with Cantor spectrum in Cuntz algebras

Key Points

• To demonstrate the existence of C*-diagonals with a Cantor spectrum in Cuntz algebras and explore their implications for related algebras.
• Proved existence of C*-diagonals in Cuntz algebra O_k for 2 ≤ k < ∞
• Generalized methods to an uncountable family of UCT Kirchberg algebras
• Constructed principal étale groupoid models for Cuntz and Kirchberg algebras
• Established a C*-diagonal with Cantor spectrum in specified Cuntz algebras
• Showed implications for distinct K-theory in UCT Kirchberg algebras
• Developed models for understanding these algebras through étale groupoid structures