Pointed Hopf Algebras of Discrete Corepresentation Type

TL;DR

This paper classifies a specific class of pointed Hopf algebras over algebraically closed fields of characteristic zero, providing explicit algebra structures and showing they are crossed products of a component and a group algebra.

Contribution

It offers a complete classification of pointed Hopf algebras of discrete corepresentation type and explicitly describes their algebra structures.

Findings

Classification of pointed Hopf algebras of discrete corepresentation type

Explicit determination of algebra structures up to isomorphism

Identification of these algebras as crossed products

Abstract

We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$, we explicitly determine the algebra structure up to isomorphism for the link indecomposable component $B$ containing the unit. It turns out that $H$ is a crossed product of $B$ and a certain group algebra.