Examples of finite-dimensional pointed Hopf algebras in characteristic $2$

TL;DR

This paper constructs new finite-dimensional pointed Hopf algebras over fields of characteristic 2 by exploring Nichols algebras from non-diagonal braided vector spaces, extending known classifications from odd characteristic fields.

Contribution

It introduces novel examples of Nichols algebras in characteristic 2 that are not of diagonal type and derives new finite-dimensional pointed Hopf algebras via bosonization.

Findings

New finite-dimensional Nichols algebras in characteristic 2

Examples from non-diagonal braided vector spaces

Construction of new pointed Hopf algebras

Abstract

We present new examples of finite-dimensional Nichols algebra over fields of characteristic 2 starting from braided vector spaces that are not of diagonal type, admit realizations as Yetter-Drinfeld modules over finite abelian groups and are analogous to braidings over fields of odd characteristic with finite-dimensional Nichols algebras presented in arXiv:1905.03074. As these last ones, they are related to the Nichols algebras of finite Gelfand-Kirillov dimension in characteristic 0 described in arXiv:1606.02521. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.