Simple Yetter-Drinfeld modules over Generalized Liu algebras

TL;DR

This paper classifies all simple Yetter-Drinfeld modules over generalized Liu algebras, showing they are finite-dimensional and identifying which have finite-dimensional Nichols algebras, advancing understanding of their module structure.

Contribution

It provides an explicit classification of simple Yetter-Drinfeld modules over generalized Liu algebras and characterizes those with finite-dimensional Nichols algebras.

Findings

All simple Yetter-Drinfeld modules are finite-dimensional.

Explicit classification of these modules is provided.

Criteria for finite-dimensional Nichols algebras are determined.

Abstract

Let $H$ be a generalized Liu algebra over an algebraically closed field $k$ of characteristic zero. We prove that all simple Yetter-Drinfeld modules over $H$ are finite-dimensional and present an explicit classification of these modules. Moreover, we completely determine which of them admit a finite-dimensional Nichols algebra.