Algebra deformations of the Hopf algebra $\mathcal{H}_1$

Alice Fialowski (1) , Friedrich Wagemann (2)

1 Department of Mathematics
2 LMJL - Laboratoire de Mathématiques Jean Leray

We 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.

Mots clés: Connes-Moscovici's Hopf algebra; associative deformations; Hochschild cohomology; Rankin-Cohen starproduct; Feigin-Fuks spectral sequence; Hochschild-Serre spectral sequence

Domaines: Algèbres quantiques [math.QA]; K-théorie et homologie [math.KT]

Alice Fialowski, Friedrich Wagemann. Algebra deformations of the Hopf algebra $\mathcal{H}_1$. Journal of Algebra, 2010, 323 (7), pp.2026-2040. ⟨10.1016/j.jalgebra.2009.12.033⟩. ⟨hal-00318644⟩