# Part III, Free Actions of Compact Quantum Groups on C*-Algebras

## TL;DR

This paper classifies free actions of compact quantum groups on unital C*-algebras using generalized factor systems and demonstrates that all finite coverings of irrational rotation C*-algebras are cleft.

## Contribution

Introduces a classification framework for free actions of compact quantum groups and applies it to show all finite coverings of irrational rotation C*-algebras are cleft.

## Key findings

- Classification of free actions via generalized factor systems
- All finite coverings of irrational rotation C*-algebras are cleft
- Provides tools for analyzing quantum symmetries in C*-algebras

## Abstract

We study and classify free actions of compact quantum groups on unital C*-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation C*-algebras are cleft.