{
  "abstract": "Let $Γ,Δ$ be finite simplicial graphs, and assume that $Γ$ has no induced squares. We prove that the right-angled Artin group $A(Δ)$ measurably embeds into $A(Γ)$ if and only if $A(Δ)$ embeds as a subgroup in a graph product of free abelian groups over $Γ$. This in turn has a graph-theoretical characterisation which can be checked algorithmically. If additionally $A(Γ)$ and $A(Δ)$ have cohomological dimension equal to two and $A(Γ)$ is not isomorphic to $\\mathbb{Z}\\times F_n$, we get that $A(Δ)$ measurably embeds into $A(Γ)$ if and only if it embeds as a subgroup in $A(Γ)$. Our proof relies on the following algebraic statement. Let $K_1,\\dots,K_n$ be a family of pairwise disjoint cliques in the square-free graph $Γ$, and let $g_1,\\dots,g_n$ be elements of $A(Γ)$ with respective parabolic supports $A(K_1),\\dots,A(K_n)$. Then the subgroup of $A(Γ)$ generated by $g_1,\\dots,g_n$ is a right-angled Artin group, where the only relations impose that $g_i$ and $g_j$ commute if $K_i\\cup K_j$ is contained in a clique of $Γ$. The same holds true more generally for pairwise disjoint cliques $K_1,\\dots,K_n$ in the extension graph $Γ^{\\mathrm{ext}}$, up to possibly replacing the elements $g_i$ by powers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15733",
  "author_total": 3,
  "authors": [
    {
      "name": "Adrien Abgrall"
    },
    {
      "name": "Alexandra Gurieva"
    },
    {
      "name": "Camille Horbez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbtjcmhb3dzzw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15733",
  "fulltext_url": null,
  "id": "bbtjcmhb3dzzw",
  "issns": [],
  "landing_url": "https://hal.science/hal-05842967v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213320511",
  "pdf_url": "https://hal.science/hal-05842967/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbtjcmhb3dzzw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05842967",
      "source": "hal",
      "url": "https://hal.science/hal-05842967v1"
    },
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.15733",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15733"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Algebraic and measurable embeddings between square-free right-angled Artin groups",
  "title_text": "Algebraic and measurable embeddings between square-free right-angled Artin groups",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bbtjcmhb3dzzw",
  "venue": "HAL",
  "versions": []
}