Liftings of Nichols algebras of type $B_3$

TL;DR

This paper explicitly classifies all finite-dimensional pointed Hopf algebras that are liftings of Nichols algebras of type B3 over finite abelian groups, providing a comprehensive understanding of their structure.

Contribution

It offers an explicit presentation of all such liftings, completing the classification for Nichols algebras of diagonal Cartan type B3.

Findings

Explicit presentations of all liftings of Nichols algebras of type B3.

Complete classification over algebraically closed fields of characteristic zero.

Structural insights into finite-dimensional pointed Hopf algebras.

Abstract

We give an explicit presentation of a family of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero that constitute all liftings of Nichols algebras of diagonal Cartan type $B_{3}$ over a finite abelian group.