Part II, Free Actions of Compact Groups on C*-Algebras

TL;DR

This paper investigates a specific class of free actions of non-Abelian compact groups on unital C*-algebras, called cleft actions, providing a classification and linking them to classical principal bundles.

Contribution

It introduces and classifies cleft actions of non-Abelian groups on C*-algebras, connecting noncommutative vector bundles to classical bundle theory.

Findings

Cleft actions are characterized by trivial associated noncommutative vector bundles.

A complete classification theory for cleft actions is developed.

Relations between cleft actions and classical principal bundles are established.

Abstract

We study a simple subclass of free actions of non-Abelian groups on unital C*-algebras, namely cleft actions. These are characterized by the fact that the associated noncommutative vector bundles are trivial. In particular, we provide a complete classification theory for these actions and describe its relations to classical principal bundles.