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arXiv · 2305.11810

Right-angled Artin groups are symmetric diagram groups

Paolo Bellingeri·Anthony Genevois·Neha Nanda
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Abstract

In this article, we show that, for every $n \geq 2$, 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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Paolo Bellingeri, Anthony Genevois, Neha Nanda. 2023-05-19. Right-angled Artin groups are symmetric diagram groups. https://arxiv.org/abs/2305.11810

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