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

Abstract

In this note, we characterise when the kernel of a rational character of a right-angled 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 Bestiva–Brady kernels and provide an algebraic proof for the results proven by Meier, Meinert and VanWyk.