Invariant subsets under compact quantum group actions
Mathematics - Operator Algebras | 46L65 (Primary), 16W22 (Secondary) | Mathematics - Quantum Algebra
arxiv: Mathematics::General Topology
We investigate compact quantum group actions on unital $C^*$-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.