Quasi-free actions of finite groups on the Cuntz algebra $\mathcal{O}_\infty$

TL;DR

This paper proves that all faithful quasi-free actions of finite groups on the Cuntz algebra  are essentially the same and can be approximated by simpler actions, revealing their structural uniformity.

Contribution

It establishes the conjugacy and asymptotic representability of all faithful quasi-free actions of finite groups on , a significant classification result.

Findings

All faithful quasi-free actions are mutually conjugate.

Such actions are asymptotically representable.

The results unify the understanding of group actions on .

Abstract

We show that any faithful quasi-free actions of a finite group on the Cuntz algebra $\mathcal{O}_\infty$ are mutually conjugate, and that they are asymptotically representable.