Hopf algebras with the dual Chevalley property of discrete corepresentation type

TL;DR

This paper classifies a specific class of Hopf algebras with the dual Chevalley property, characterizes their link quivers, and constructs an explicit infinite-dimensional example with particular properties.

Contribution

It provides a classification framework for Hopf algebras with the dual Chevalley property of discrete corepresentation type and constructs a novel infinite-dimensional example.

Findings

Characterization of link quivers for these Hopf algebras

Determination of structures of link-indecomposable components

Construction of a new infinite-dimensional non-pointed non-cosemisimple Hopf algebra

Abstract

We try to classify Hopf algebras with the dual Chevalley property of discrete corepresentation type over an algebraically closed field $\Bbb{k}$ with characteristic 0. For such Hopf algebra $H$, we characterize the link quiver of $H$ and determine the structures of the link-indecomposable component $H_{(1)}$ containing $\Bbb{k}1$. Besides, we construct an infinite-dimensional non-pointed non-cosemisimple link-indecomposable Hopf algebra $H(e_{\pm 1}, f_{\pm 1}, u, v)$ with the dual Chevalley property of discrete corepresentation type.