Rigidity of action of compact quantum groups III: the general case

Abstract

If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a natural bimodule morphism on the module of sections of the co-tangent bundle, then it is proved that the quantum group is necessarily commutative as a $C^{\ast }$ algebra i.e. isomorphic with $C(G)$ for some compact group $G$. From this, we deduce that the quantum isometry group of such a manifold M coincides with $C(ISO(M))$ where $ISO(M)$ is the group of (classical) isometries, i.e. there is no genuine quantum isometry of such a manifold.

Withdrawn because its content is now subsumed and generalized in arXiv:1309.1294 and arXiv:1410.8650

References in corpus (1)

• Rigidity of action of compact quantum groups II

Cited by in corpus (2)

• Invariant subsets under compact quantum group actions
• On the problem of classifying simple compact quantum groups