# On non-connected pointed Hopf algebras of dimension 16 in characteristic 2

## TL;DR

This paper classifies all non-connected pointed Hopf algebras of dimension 16 over an algebraically closed field of characteristic 2, revealing infinitely many new non-commutative, non-cocommutative examples.

## Contribution

It provides a complete classification of such Hopf algebras, including infinitely many new examples, expanding understanding of their structure in characteristic 2.

## Key findings

- Infinitely many classes of pointed Hopf algebras of dimension 16
- Existence of infinitely many new non-commutative, non-cocommutative examples
- Classification includes algebras generated by group-like and skew-primitive elements

## Abstract

Let $\mathbb{k}$ be an algebraically closed field. We give a complete classification of non-connected pointed Hopf algebras of dimension $16$ with char$\,\mathbb{k}=2$ that are generated by group-like elements and skew-primitive elements. It turns out that there are infinitely many classes (up to isomorphism) of pointed Hopf algebras of dimension 16. In particular, we obtain infinitely many new examples of non-commutative non-cocommutative finite-dimensional pointed Hopf algebras.