Rank three Nichols algebras of diagonal type over fields of positive characteristic

TL;DR

This paper classifies all rank three Nichols algebras of diagonal type with finite root systems over fields of any characteristic, expanding understanding in algebraic structures related to quantum groups.

Contribution

It provides a complete classification of rank three Nichols algebras of diagonal type over fields of positive characteristic, utilizing finite Weyl groupoid classification.

Findings

Complete classification of rank three Nichols algebras of diagonal type.

Identification of finite root systems in these algebras.

Application of Weyl groupoid classification to positive characteristic fields.

Abstract

Over fields of arbitrary characteristic we classify all rank three Nichols algebras of diagonal type with a finite root system. Our proof uses the classification of the finite Weyl groupoids of rank three.