2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225694We compute the second Hochschild cohomology space $HH^2(\mathcal{H}_1)$ of Connes-Moscovici's Hopf algebra $\mathcal{H}_1$, giving the infinitesimal deformations (up to equivalence) of the associative structure. $HH^2(\mathcal{H}_1)$ 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 pagesQuantum AlgebraAlgebraic Geometry17B65; 17B56; 16E40; 16S80text