Liftings of Jordan and super Jordan planes

TL;DR

This paper classifies certain finite-dimensional pointed Hopf algebras with specific infinitesimal braiding structures, identifying new classes as liftings of Jordan or super Jordan planes over particular groups.

Contribution

It provides a classification of new pointed Hopf algebras with non-diagonal infinitesimal braiding of dimension 2, expanding understanding of their structure and origins.

Findings

Identified new classes of Hopf algebras as liftings of Jordan and super Jordan planes

Classified pointed Hopf algebras with non-diagonal infinitesimal braiding of dimension 2

Connected these algebras to nilpotent-by-finite groups

Abstract

We classify pointed Hopf algebras with finite Gelfand-Kirillov dimension whose infinitesimal braiding has dimension 2 but is not of diagonal type, or equivalently is a block. These Hopf algebras are new and turn out to be liftings of either a Jordan or a super Jordan plane over a nilpotent-by-finite group.