Free actions of compact quantum group on unital C*-algebras

Abstract

Let F be a field, G a finite group, and Map(G,F) the Hopf algebra of all set-theoretic maps G->F. If E is a finite field extension of F and G is its Galois group, the extension is Galois if and only if the canonical map resulting from viewing E as a Map(G,F)-comodule is an isomorphism. Similarly, a finite covering space is regular if and only if the analogous canonical map is an isomorphism. In this paper we extend this point of view to actions of compact quantum groups on unital C*-algebras. We prove that such an action is free if and only if the canonical map (obtained using the underlying Hopf algebra of the compact quantum group) is an isomorphism. In particular, we are able to express the freeness of a compact Hausdorff topological group action on a compact Hausdorff topological space in algebraic terms.

References in corpus (3)

• Galois-Type Extensions and Equivariant Projectivity
• Equivariant Join and Fusion of Noncommutative Algebras
• Local Proof of Algebraic Characterization of Free Actions

Cited by in corpus (15)

• Equivariant Join and Fusion of Noncommutative Algebras
• Spectral triples for noncommutative solenoidal spaces from self-coverings
• Free Actions on C*-algebra Suspensions and Joins by Finite Cyclic Groups
• Part I, Free Actions of Compact Abelian Groups on C*-Algebras
• Rank-two Milnor idempotents for the multipullback quantum complex projective plane
• Categorically Morita equivalent compact quantum groups
• Local Proof of Algebraic Characterization of Free Actions
• Dirac operators on noncommutative principal torus bundles
• Noncommutative Coverings of Quantum Tori
• Noncommutative bundles over the multi-pullback quantum complex projective plane
• Fixed Point Algebras for Easy Quantum Groups
• Noncommutative Borsuk-Ulam-type conjectures revisited
• Part III, Free Actions of Compact Quantum Groups on C*-Algebras
• Classical gauge theory on quantum principal bundles
• Nontrivial Deformation of a Trivial Bundle