{
  "abstract": "In this paper, we provide a comprehensive study of the structural properties of the transposed Poisson algebra $\\mathcal{W}(a,-1)$. We classify several types of linear maps, including derivations, local derivations, quasi-derivations, and $δ$-derivations, showing that non-trivial $δ$-derivations exist only for $δ=1$ and $δ=\\frac{1}{2}$. Furthermore, we describe the groups of automorphisms, local automorphisms, 2-local automorphisms, and quasi-automorphisms. We also investigate Rota--Baxter operators of weight $1$ on $\\mathcal{W}(a,-1)$. Specifically, we classify operators that are homogeneous with respect to both the standard $\\mathbf{Z}$-grading and a $\\mathbf{Z}_2$-grading, establishing a rigidity result for the latter case. Finally, we classify all $\\mathbf{W}$-compatible Novikov--Poisson structures, demonstrating that the associative product on the Witt algebra is universally compatible with its known Novikov structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.20584",
  "author_total": 2,
  "authors": [
    {
      "name": "Roman Lubkov"
    },
    {
      "name": "Ilya Shiringovskiy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftveb6am53xgp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.20584",
  "fulltext_url": null,
  "id": "ftveb6am53xgp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.20584",
  "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.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.20584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftveb6am53xgp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2606.20584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.20584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Transposed Poisson structure on the Witt-type algebra $\\mathcal{W}(a,-1)$: Derivations, Automorphisms, and Rota--Baxter operators",
  "title_text": "Transposed Poisson structure on the Witt-type algebra 𝒲(a,−1): Derivations, Automorphisms, and Rota--Baxter operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/ftveb6am53xgp",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.46298/cm.18245",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}