The Connes embedding problem (CEP) is a in the theory of tracial von Neumann algebras and asks whether or not every algebra embeds into an ultrapower hyperfinite II 1 <mml:annotation encoding="application/x-...

In his celebrated paper in 1976, A. Connes casually remarked that any finite von Neumann algebra ought to be embedded into an ultraproduct of matrix algebras, which is now known as the Connes embedding conjecture or problem. This conjecture became one of the central open problems in the field of operator algebras since E. Kirchberg’s seminal work in 1993 that proves it is equivalent to a variet...

We construct a universal deformation formula for Connes-Moscovici’s Hopf algebra without any projective structure using Fedosov’s quantization of symplectic diffeomorphisms.