Right-angled Artin groups are symmetric diagram groups

Abstract

In this article, we show that, for every $n\ge 2$, the pure virtual twin group $PV{T}_n$ can be naturally described as a symmetric diagram group, a family of groups introduced by V. Guba and M. Sapir and associated to semigroup presentations. Inspired by this observation, we prove that every finitely generated right-angled Artin group is a symmetric diagram group. This contrasts with the fact that not all right-angled Artin groups are planar diagram groups.

17 pages, 10 figures. Comments are welcome!