A note on the injectivity of actions of compact quantum groups on a class of $C^{\ast }$-algebras
Volume 120 / 2020
Banach Center Publications 120 (2020), 71-79
MSC: 81R50, 81R60, 20G42, 58B34.
DOI: 10.4064/bc120-6
Abstract
We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{\ast }$-algebras. 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 deformations of compact, smooth manifolds.
