Higher rank Nichols algebras of diagonal type with finite arithmetic root systems in positive characteristic

TL;DR

This paper classifies higher rank Nichols algebras of diagonal type with finite arithmetic root systems over fields of positive characteristic, advancing the understanding of pointed Hopf algebras.

Contribution

It provides a complete classification of rank ≥ 5 Nichols algebras of diagonal type with finite root systems in positive characteristic.

Findings

Classified all such Nichols algebras for rank ≥ 5

Used Weyl groupoids and arithmetic root systems as key tools

Extended classification results to positive characteristic fields

Abstract

The classification of Nichols algebras is an essential step in the classification theory of pointed Hopf algebras by lifting method of N. Andruskiewitsch and H.-J. Schneider. Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. In this paper, all rank $r\geq 5$ Nichols algebras of diagonal type with a finite irreducible root system over fields of positive characteristic are classified. Weyl groupoids and finite arithmetic root systems are crucial tools for our classification.