Faithful compact quantum group actions on connected compact metrizable spaces

Abstract

We construct faithful actions of quantum permutation groups on connected compact metrizable spaces. This disproves a conjecture of Goswami.

8 pages

References in corpus (5)

• Quantum Symmetry Groups of Finite Spaces
• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups
• Quantum Group of Isometries in Classical and Noncommutative Geometry
• Ergodic Actions of Universal Quantum Groups on Operator Algebras
• Rigidity of action of compact quantum groups II

Cited by in corpus (10)

• Rigidity of action of compact quantum groups II
• Existence and examples of quantum isometry group for a class of compact metric spaces
• Faithful actions of locally compact quantum groups on classical spaces
• Tannaka-Krein reconstruction and ergodic actions of easy quantum groups
• Invariant subsets under compact quantum group actions
• The Nodal Cubic is a Quantum Homogeneous Space
• On the problem of classifying simple compact quantum groups
• Quantum symmetry groups of Hilbert modules equipped with orthogonal filtrations
• An averaging trick for smooth actions of compact quantum groups on manifolds
• A note on the injectivity of action by compact quantum groups on a class of $C^{\ast }$-algebras