Separable cowreaths in higher dimension

Abstract

In this paper we present an infinite family of (h-)separable cowreaths with increasing dimension. Menini and Torrecillas proved in [20] that for $A=Cl(\alpha,\beta, \gamma)$, a four-dimensional Clifford algebra, and $H=H_4$, Sweedler's Hopf algebra, the cowreath $(A \otimes H^{op},H, \psi)$ is always (h-)separable. We show how to produce similar examples in higher dimension by considering a $2^{n+1}$-dimensional Clifford algebra $A=Cl(\alpha,\beta_i,\gamma_i,\lambda_{ij})$ and $H=E(n)$, a suitable pointed Hopf algebra that generalizes $H_4$. We adopt the approach pursued in [19], requiring that the separability morphism be of a simplified form, which in turn forces the defining scalars $\alpha,\beta_i,\gamma_i,\lambda_{ij}$ to satisfy further conditions.