Classification of quasi-free compact group actions on Cuntz algebras

TL;DR

This paper classifies quasi-free actions of finite groups on Cuntz algebras using representation ring data and provides partial results for compact groups, advancing understanding of symmetries in operator algebras.

Contribution

It introduces a classification method for finite group actions on Cuntz algebras based on representation ring data and extends some results to compact groups.

Findings

Finite group actions classified by representation ring data.

Partial classification results for compact group actions.

Enhanced understanding of symmetries in Cuntz algebras.

Abstract

Quasi-free actions of finite groups on Cuntz algebras $\mathcal O_n$ for $n\geq 2$ are classified up to conjugacy by data in the representation ring. Partial results are obtained for quasi-free actions by compact groups.