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

References in corpus (22)

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

Cited by in corpus (7)

• Lifting spectral triples to noncommutative principal bundles
• Noncommutative Coverings of Quantum Tori
• Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds
• A Note on Twisted Crossed Products and Spectral Triples
• Part III, Free Actions of Compact Quantum Groups on C*-Algebras
• An Atiyah Sequence for Noncommutative Principal Bundles
• Realizations of free actions via their fixed point algebras