Nichols algebras of group type with many quadratic relations

TL;DR

This paper classifies finite-dimensional Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups with specific quadratic relation constraints, revealing a new algebra in characteristic two.

Contribution

It provides a complete classification of such Nichols algebras and introduces a previously unknown finite-dimensional example in characteristic two.

Findings

All classified Nichols algebras are finite-dimensional.

The classification includes all known finite-dimensional Nichols algebras of nonabelian group type.

A new finite-dimensional Nichols algebra over fields of characteristic two is discovered.

Abstract

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known finite-dimensional Nichols algebras of nonabelian group type appear in the result of our classification. We find a new finite-dimensional Nichols algebra over fields of characteristic two.