Associative algebra deformations of the Connes-Moscovici's Hopf algebra ${\mathcal{H}}_1$

Abstract

We compute the second Hochschild cohomology space $H{H}^2({\mathcal{H}}_1)$ of Connes-Moscovici's Hopf algebra ${\mathcal{H}}_1$, giving the infinitesimal deformations (up to equivalence) of the associative structure. $H{H}^2({\mathcal{H}}_1)$ is shown to be one dimensional, and thus Connes-Moscovici's formal deformation of ${\mathcal{H}}_1$ using Rankin-Cohen brackets is unique up to equivalence.

14 pages

References in corpus (1)

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