Presentation of kernels of rational characters of right-angled Artin groups

TL;DR

This paper characterizes when the kernels of rational characters of right-angled Artin groups are finitely generated and presented, providing explicit generators and presentations, and generalizing previous results by Dicks, Leary, Meier, Meinert, and VanWyk.

Contribution

It offers a complete algebraic characterization and explicit presentations for kernels of rational characters of right-angled Artin groups, extending prior work.

Findings

Identifies conditions for finite generation and presentation of kernels

Provides explicit generating sets and presentations

Generalizes previous results on Bestvina-Brady groups

Abstract

In this note, we characterise when the kernel of a rational character of a right-anlged Artin group, also known as generalised Bestiva-Brady group, is finitely generated and finitely presented. In these cases, we exhibit a finite generating set and a presentation. These results generalise Dicks and Leary's presentations of Bestina-Brady kernels and provide an algebraic proof for the results proven by Meier, Meinert, and VanWyk.