New examples of separable cowreaths over Clifford algebras

TL;DR

This paper explores conditions for separability of a specific cowreath algebra constructed from an 8-dimensional Clifford algebra and a ribbon Hopf algebra, extending previous research in the area.

Contribution

It provides new criteria for separability of cowreaths over Clifford algebras using the structure of the Hopf algebra E(2).

Findings

Identifies separability conditions for cowreaths over Clifford algebras.

Extends previous work on cowreaths and Hopf algebras.

Provides explicit examples involving 8-dimensional Clifford algebras.

Abstract

This paper continues the research we developed in \cite{MT1} and \cite% {MT2}. The main aim of this paper is to investigate separability conditions for a cowreath $(A\otimes H^{op},H,\psi )$ constructed by using the $8$% -dimensional Clifford algebra $A=Cl(\alpha ,\beta _{1},\beta _{2},\gamma _{1},\gamma _{2},\lambda )$ considered as an $H$-comodulo algebra where $H$ is the $8$-dimensional unimodular ribbon Hopf algebra $E(2)$ introduced by Radford in \cite{R}.