Root multiplicities for Nichols algebras of diagonal type of rank two

TL;DR

This paper calculates the multiplicities of certain roots in rank two Nichols algebras of diagonal type, providing explicit descriptions of root vectors and algebra relations.

Contribution

It offers a detailed determination of root multiplicities and root vectors for rank two Nichols algebras, advancing understanding of their algebraic structure.

Findings

Explicit root multiplicities for a class of roots identified

Root vectors corresponding to these roots characterized

Relations of the Nichols algebra in specific degrees described

Abstract

We determine the multiplicities of a class of roots for Nichols algebras of diagonal type of rank two, and identify the corresponding root vectors. Our analysis is based on a precise description of the relations of the Nichols algebra in the corresponding degrees.