{
  "abstract": "For $d>3$ we construct the product of the bosonic on-shell higher-spin algebra directly on the AdS-traceless representatives. We find the traceless projector in closed form, determine all linear relations among the trace-producing operators, and prove that every class modulo the $\\mathfrak{sp}(2)$ ideal has a unique traceless representative. The resulting product is an explicit differential operator, which we test on the $\\mathfrak{so}(d-1,2)$ generators. A toy model shows how the factorisation lifts from bilinear products to trilinear ones in minimal $A_\\infty$-algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26704",
  "author_total": 1,
  "authors": [
    {
      "name": "M. A. Povarnin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dfe526tp4zz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26704",
  "fulltext_url": null,
  "id": "0dfe526tp4zz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26704",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7222998848",
  "pdf_url": "https://arxiv.org/pdf/2610.26704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dfe526tp4zz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26704"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "An explicit product for the on-shell higher-spin algebra in $AdS_d$-space",
  "title_text": "An explicit product for the on-shell higher-spin algebra in AdS_d-space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/0dfe526tp4zz9",
  "venue": "arXiv",
  "versions": []
}