Annihilator ideals of indecomposable modules of finite-dimensional pointed Hopf algebras of rank one

TL;DR

This paper classifies all annihilator ideals of indecomposable modules over finite-dimensional pointed Hopf algebras of rank one, providing explicit generators and a classification for nilpotent type cases over the Klein 4-group.

Contribution

It offers a complete description of annihilator ideals for indecomposable modules of rank one pointed Hopf algebras, including a classification for nilpotent type over Klein 4-group.

Findings

All annihilator ideals of indecomposable modules are explicitly described by generators.

Classification of ideals for nilpotent type over Klein 4-group is provided.

The structure of modules and their annihilators in these algebras is fully characterized.

Abstract

Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero. In this paper we describe all annihilator ideals of indecomposable H-modules by generators. In particular, we give the classification of all ideals of finite-dimensional pointed Hopf algebra of rank one of nilpotent type over Klein 4-group.