# Examples of finite-dimensional pointed Hopf algebras in positive characteristic

## TL;DR

This paper introduces new finite-dimensional Nichols algebras over fields of positive characteristic, expanding the known examples of pointed Hopf algebras with non-diagonal braidings and finite Gelfand-Kirillov dimension.

## Contribution

It provides novel examples of Nichols algebras in positive characteristic that are not of diagonal type and constructs associated pointed Hopf algebras via bosonization.

## Key findings

- New finite-dimensional Nichols algebras over positive characteristic fields.
- Existence of non-diagonal braided vector spaces realized as Yetter-Drinfeld modules.
- Construction of finite-dimensional pointed Hopf algebras from these Nichols algebras.

## Abstract

We present new examples of finite-dimensional Nichols algebras over fields of positive characteristic. The corresponding braided vector spaces are not of diagonal type, admit a realization as Yetter-Drinfeld modules over finite abelian groups and are analogous to braidings over fields of characteristic zero whose Nichols algebras have finite Gelfand-Kirillov dimension described in arXiv:1606.02521. We obtain nex examples of finite-dimensional pointed Hopf algebras by bosonization with group algebras of suitable finite abelian groups.