Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras

TL;DR

This paper explores the structure of generic base and universal comodule algebras for specific finite-dimensional Hopf algebras, providing explicit descriptions for classes like Taft algebras and E(n).

Contribution

It explicitly determines the generic base and universal comodule algebras for several important classes of finite-dimensional Hopf algebras.

Findings

Explicit descriptions for Taft algebras

Descriptions for E(n) Hopf algebras

Analysis of monomial Hopf algebras

Abstract

After recalling the definitions and the properties of the generic base algebra and of the universal comodule algebra attached to a Hopf algebra by Aljadeff and the second-named author, we determine these algebras for the Taft algebras, the Hopf algebras E(n), and certain monomial Hopf algebras.