A universal deformation formula for Connes-Moscovici's Hopf algebra without any projective structure

TL;DR

This paper develops a universal deformation formula for Connes-Moscovici's Hopf algebra utilizing Fedosov's quantization, expanding the algebra's applicability without requiring projective structures.

Contribution

It introduces a novel deformation formula for Connes-Moscovici's Hopf algebra that does not depend on projective structures, using Fedosov's quantization techniques.

Findings

Constructed a universal deformation formula for the Hopf algebra

Applied Fedosov's quantization to symplectic diffeomorphisms

Eliminated the need for projective structures in the deformation process

Abstract

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