Embeddings of right-angled Artin groups

TL;DR

This paper constructs an explicit embedding of right-angled Artin groups into classical pure braid groups, enabling new insights into their structure and relationships with other Artin groups.

Contribution

It provides the first explicit embedding of right-angled Artin groups into pure braid groups, facilitating the study of their algebraic properties and subgroup structures.

Findings

Explicit embedding of right-angled Artin groups into pure braid groups

Corollaries on embeddings of arbitrary Artin groups into right-angled Artin groups

Identification of linearly independent subgroups within right-angled Artin groups

Abstract

We explicitly construct an embedding of a right-angled Artin group into a classical pure braid group. Using this we obtain a number of corollaries describing embeddings of arbitrary Artin groups into right-angled Artin groups and linearly independent subgroups of a right-angled Artin group.