A note on the injectivity of action by compact quantum groups on a class of $C^{\ast }$-algebras

Abstract

We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{\ast }$-algebra. As an application, we prove that any faithful smooth action by a compact quantum group on a compact smooth (not necessarily connected) manifold is injective. A similar result is proved for actions on $C^{\ast }$- algebras obtained by Rieffel-deformation of compact, smooth manifolds.

arXiv admin note: text overlap with arXiv:1507.08407, arXiv:1309.1294