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 (6)

• Noncommutative Geometry Approach to Principal and Associated Bundles
• Picard groups in Poisson geometry
• Index theory for actions of compact Lie groups on C*-algebras
• Dirac operator on noncommutative principal circle bundles
• Part II, Free Actions of Compact Groups on C*-Algebras
• Quantum lens spaces and principal actions on graph 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