The lower central series of a right-angled Artin group

TL;DR

This paper extends classical algebraic methods to right-angled Artin groups, providing a new basis construction for their lower central series using Lyndon words and Magnus' approach.

Contribution

It introduces a novel extension of Magnus' and Lyndon words techniques to right-angled Artin groups, enabling explicit basis computation for their lower central series.

Findings

Extended Magnus' approach to RAAGs

Developed an algorithm for basis computation

Connected Lyndon words with RAAG lower central series

Abstract

We give a description of Duchamp and Krob's extension of Magnus' approach to the lower central series of the free group to right-angled Artin groups. We also describe how Lalonde's extension of Lyndon words to the partially-commutative settings gives a simple algorithm to find a basis for consecutive quotients of the lower central series of a RAAG.