Smooth actions of compact quantum groups on compact smooth manifolds

Abstract

Definition of a smooth action of a CQG on a compact, smooth manifold is given and studied. It is shown that a smooth action is always injective. Furthermore A necessary and sufficient condition for a lift of the smooth action as a bimodule morphism on the bimodule of one forms has been deduced and it is also shown to be equivalent to the condition of preserving some Riemannian inner product on the manifold.

arXiv commentThis is essentially a subset of the paper titled 'Rigidity of action of compact quantum groups on compact, connected manifolds' (arXiv:1309.1294) which is going to be split into two separate papers (one of them being the present one) for submission to journals