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

TL;DR

This paper develops a classification theory for free actions of compact Abelian groups on unital C*-algebras, linking it to classical principal bundle classification.

Contribution

It provides a complete classification framework for these group actions, connecting operator algebra theory with geometric principal bundle concepts.

Findings

Classification of free actions of compact Abelian groups on unital C*-algebras

Relation established between C*-algebra actions and principal bundle theory

Framework facilitates understanding of symmetry in operator algebras

Abstract

We study free and compact group actions on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classical classification theory of principal bundles.