On some root multiplicities for Nichols algebras of diagonal type over arbitrary fields

TL;DR

This paper generalizes the calculation of root multiplicities in Nichols algebras of diagonal type to arbitrary fields, extending previous results from characteristic zero to broader settings.

Contribution

It introduces a method to determine root multiplicities for Nichols algebras over fields of any characteristic, broadening the scope of prior characteristic-zero results.

Findings

Root multiplicities are explicitly determined over arbitrary fields.

The results extend known characteristic-zero cases.

New techniques are developed for fields of positive characteristic.

Abstract

In this paper, our main aim is to determine the multiplicities of a class of roots for Nichols algebra of diagonal type over fields of arbitrary characteristic, which is a generalization of the results on the multiplicities of these roots over fields of characteristic zero obtained by I. Heckenberber and the author.