A construction of finite index C*-algebra inclusions from free actions of compact quantum groups

Abstract

Given an action of a compact quantum group on a unital C*-algebra, one can amplify the action with an adjoint representation of the quantum group on a finite dimensional matrix algebra, and consider the resulting inclusion of fixed point algebras. We show that this inclusion is a finite index inclusion of C*-algebras when the quantum group acts freely. We show that two natural definitions for a quantum group to act freely, namely the Ellwood condition and the saturatedness condition, are equivalent.

24 pages; small changes made, also added some more comments concerning history of the topic

References in corpus (4)

• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups
• Notes on Compact Quantum Groups
• A Galois correspondence for II_1 factors and quantum groupoids
• Index theory for actions of compact Lie groups on C*-algebras

Cited by in corpus (10)

• Free actions of compact quantum group on unital C*-algebras
• Gauge theory on noncommutative Riemannian principal bundles
• Free Actions on C*-algebra Suspensions and Joins by Finite Cyclic Groups
• Part I, Free Actions of Compact Abelian Groups on C*-Algebras
• Lifting spectral triples to noncommutative principal bundles
• Categorically Morita equivalent compact quantum groups
• Fixed Point Algebras for Easy Quantum Groups
• 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