AF-embeddability of crossed products of Cuntz algebras

2001/10/09 by Takeshi Katsura, Katsura, Takeshi
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0110095

12 pages

arxiv created 2001/10/09 · openalex publication_date 2001/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our algebras become simple and purely infinite, and consequently our algebras are either purely infinite or AF-embeddable when they are simple.

Citations

• On Quasidiagonal C*-algebras
• The ideal structures of crossed products of Cuntz algebras by quasi-free actions of abelian groups

Related

• The ideal structures of crossed products of Cuntz algebras by quasi-free actions of abelian groups
• On crossed products of the Cuntz algebra \mathcal O_∞ by quasi-free actions of abelian groups
• On the AF embeddability of crossed products of AF algebras by the integers
• AF-embedding of the crossed products of AH-algebras by finitely generated abelian groups
• Partial Crossed Product Presentations For O_n and M_k(O_n) Using Amenable Groups