On the inclusion \cO₂ ⊂ \cQ₂

2025/05/22 by Jacopo Bassi, Bassi, Jacopo, Roberto Conti +1
Mathematics · #(MSC 2010) Primary: 46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Secondary: 47L40

paper · pdf · doi:10.48550/arxiv.2505.16759

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The diadic C^*-algebra \cQ₂ contains canonically a copy of the Cuntz algebra \cO₂. It is shown that the inclusion \cO₂ ⊂ \cQ₂ is C^*-irreducible and rigid. It follows that the injective envelopes of these two C^*-algebras are *-isomorphic.

Citations

• Unique Pseudo-Expectations for Hereditarily Essential C^*-Inclusions
• An approach to the study of boundary actions
• Inclusions of C^*-algebras arising from fixed-point algebras
• On simplicity of intermediate C*-algebras
• Boundaries of reduced C*-algebras of discrete groups
• The 2-adic ring C^*-algebra of the integers and its representations

Related

• OnC*-algebras generated by pairs ofq-commuting isometries
• C^*-algebras generated by the paths semigroup
• Complete isometries into C*-algebras
• A construction of C^*-algebras from C^*-correspondences
• On simplicity of Cuntz algebra and its generalizations