Abelian splittings of Right-Angled Artin Groups

TL;DR

This paper characterizes the conditions under which right-angled Artin groups can be nontrivially decomposed over abelian subgroups, providing insights into their algebraic structure.

Contribution

It offers a complete characterization of abelian splittings in right-angled Artin groups, advancing understanding of their algebraic decompositions.

Findings

Identifies criteria for nontrivial abelian splittings

Provides a classification of splittings based on group properties

Enhances understanding of the structure of right-angled Artin groups

Abstract

We characterize when (and how) a Right-Angled Artin group splits nontrivially over an abelian subgroup.