Right-angled Artin groups are symmetric diagram groups

2023/05/19 by Paolo Bellingeri, Bellingeri, Paolo, Anthony Genevois +3
Mathematics · #05C25 #20F36 #20F65 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2305.11810

openalex publication_date 2023/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we show that, for every n ≥ 2, the pure virtual twin group PVT_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.

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• An introduction to right-angled Artin groups
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• Twisted right-angled Artin groups