Realization of hyperbolic group C*-algebras as decreasing intersection of Cuntz algebras O_2

TL;DR

This paper demonstrates that for certain ICC groups embeddable into hyperbolic groups, their reduced group C*-algebras can be expressed as decreasing intersections of Cuntz algebra O_2 isomorphs, using boundary action analysis.

Contribution

It establishes a novel representation of reduced group C*-algebras as intersections of Cuntz algebras for a class of hyperbolic-related groups.

Findings

Reduced group C*-algebras are intersections of O_2 isomorphs.

Applicable to ICC groups embeddable into hyperbolic groups.

Uses boundary action amenability to prove results.

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 O_2. The proof is based on the study of amenable quotients of the boundary actions.