{
  "abstract": "We examine the differential geometry of Lie semiheaps that admit biunital elements. Open Ol'shanskii semigroups, which appear widely across causal geometry and harmonic analysis, provide a large class of examples. It is shown that the subset of biunits is a smoothly embedded Lie subheap. Moreover, there is a canonical Lie triple algebroid associated with any proper biunital Lie semiheap. That is, there is a vector bundle over the manifold of biunits that comes equipped with a ternary bracket that satisfies the axioms of a Lie triple system together with a compatible `higher' anchor map. Although every Lie triple algebroid associated with a proper biunital Lie semiheap is trivialisable, it is not canonically so, unlike the case of the tangent bundle of a Lie group. As concrete examples, we examine the Lie semiheap of real $n\\times n$ matrices, and the conformal causal Lie semiheap associated with the Lie group $\\mathrm{SU}(2,2)$, which is a double cover of the conformal group of Minkowski spacetime, and the future-directed light cone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00812",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrew James Bruce"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/depsvgb4thdyy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00812",
  "fulltext_url": null,
  "id": "depsvgb4thdyy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00812",
  "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-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/depsvgb4thdyy.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Biunital Lie Semiheaps and Lie Triple Systems",
  "title_text": "Biunital Lie Semiheaps and Lie Triple Systems",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/depsvgb4thdyy",
  "venue": "arXiv",
  "versions": []
}