Twist star products and Morita equivalence

Abstract

We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star products cannot both exist on the same manifold M. This implies, for example, that there is no symplectic star product on the projective space CPn−1 induced by a twist based on U(gln(C))〚h〛 or any sub-bialgebra, for every n≥2.