# Pointed Hopf algebras over non abelian groups with decomposable braidings, I

## TL;DR

This paper classifies certain finite-dimensional pointed Hopf algebras with specific decomposable braidings over non-abelian groups, providing presentations and confirming a key conjecture in the field.

## Contribution

It offers a complete description and presentation of these Hopf algebras and verifies the Andruskiewitsch-Schneider Conjecture for this class.

## Key findings

- Classification of pointed Hopf algebras with decomposable braidings
- Explicit generators and relations for the Nichols algebra
- Verification of the Andruskiewitsch-Schneider Conjecture

## Abstract

We describe all finite-dimensional pointed Hopf algebras whose infinitesimal braiding is a fixed Yetter-Drinfeld module decomposed as the sum of two simple objects: a point and the one of transpositions of the symmetric group in three letters. We give a presentation by generators and relations of the corresponding Nichols algebra and show that Andruskiewitsch-Schneider Conjecture holds for this kind of pointed Hopf algebras.