Realization of hyperbolic group C*-algebras as decreasing intersection of Cuntz algebras O₂

2014/06/10 by Yuhei Suzuki, Suzuki, Yuhei
Mathematics · #20F67 #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.DS #math.GR #math.OA #msc:20F67 #msc:46L05

paper · pdf · doi:10.48550/arxiv.1406.2740

11 pages

arxiv created 2014/06/10 · openalex publication_date 2014/06/10 · arxiv updated 2014/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that for every ICC group which is embeddable into a hyperbolic group, the reduced group C*-algebra is realized as the intersection of a decreasing sequence of isomorphs of the Cuntz algebra O₂. The proof is based on the study of amenable quotients of the boundary actions.

Related

• Note on C*-algebras associated to boundary actions of hyperbolic 3-manifold groups
• New holomorphically closed subalgebras of C^*-algebras of hyperbolic groups
• Cuntz-Li relations, Inverse semigroups and Groupoids
• The Cuntz semigroup as an invariant for C*-algebras
• Inverse semigroups and the Cuntz-Li algebras