A Super Version of the Connes-Moscovici Hopf Algebra

Abstract

We define a super version of the Connes-Moscovici Hopf algebra, ${\mathcal{H}}_1$. For that, we consider the supergroup $G^s=Dif{f}^{+}({\mathbb{R}}^{1,1})$ of orientation preserving diffeomorphisms of the superline ${\mathbb{R}}^{1,1}$ and define two (super) subgroups $G_1^s$ and $G_2^s$ of $G^s$ where $G_1^s$ is the supergroup of affine transformations. The super Hopf algebra ${\mathcal{H}}_1^s$ is defined as a certain bicrossproduct super Hopf algebra of the super Hopf algebras attached to $G_1^s$ and $G_2^s$. We also give an explicit description of ${\mathcal{H}}_1^s$ in terms of generators and relations.

Dedicated to Henri Moscovici