{
  "abstract": "For an $n$-Lie--Rinehart algebra, $n>2$, the anchor is defined on $\\Aext{n-1}L$, so its kernel does not determine a distinguished submodule of $L$. We introduce the anchor radical $\\Rad(ρ)\\subset L$ and prove that it is an adjoint-stable ideal on which the bracket is $A$-multilinear. We then derive an explicit obstruction to the $A$-linearity of metric compatibility in fundamental directions. This obstruction vanishes on $\\Rad(ρ)$, whereas a strongly nondegenerate compatible metric on all of $L$ forces the anchor to vanish. These results lead to a natural notion of orthogonal structure on the anchor radical. For anchors induced by Nambu tensors, the radical is identified with the cotangent annihilator of the tensor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31538",
  "author_total": 2,
  "authors": [
    {
      "name": "Irmely Gladesh Mabanza Nsiloulou"
    },
    {
      "name": "Basile Guy Richard Bossoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fr1datqvbdz1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31538",
  "fulltext_url": null,
  "id": "5fr1datqvbdz1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31538",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7214640368",
  "pdf_url": "https://arxiv.org/pdf/2609.31538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fr1datqvbdz1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31538"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Anchor Radicals and Metric Rigidity in $n$-Lie--Rinehart Algebras",
  "title_text": "Anchor Radicals and Metric Rigidity in n-Lie--Rinehart Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/5fr1datqvbdz1",
  "venue": "arXiv",
  "versions": []
}