Invariant subsets under compact quantum group actions

Abstract

We investigate compact quantum group actions on unital $C^{\ast }$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

Examples of compact quantum group actions on compact Hausdorff spaces added. Comments are welcome

References in corpus (3)

• Faithful compact quantum group actions on connected compact metrizable spaces
• Rigidity of action of compact quantum groups II
• Rigidity of action of compact quantum groups III: the general case

Cited by in corpus (3)

• Existence and examples of quantum isometry group for a class of compact metric spaces
• Faithful actions of locally compact quantum groups on classical spaces
• Quantum Isometry group of dual of finitely generated discrete groups and quantum groups