Computing finite Weyl groupoids

TL;DR

This paper introduces algorithms for computing generalized root systems of Nichols algebras and Lie superalgebras, enabling the calculation of Lyndon words and hyperwords crucial for minimal presentations.

Contribution

It provides new algorithms to compute root systems, Lyndon words, and hyperwords for Nichols algebras and Lie superalgebras, facilitating their structural analysis.

Findings

Algorithms successfully compute generalized root systems.

Lyndon words and hyperwords can be systematically obtained.

Supports minimal presentation of finite root system Nichols algebras.

Abstract

We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis associated to each positive root, along with their corresponding hyperwords. This data is essential for obtaining a minimal presentation of Nichols algebras of diagonal type with a finite root system.