{
  "abstract": "The Schrödinger--Witt algebras are infinite-dimensional Lie algebras of local dynamical symmetries of the free Schrödinger equation; they contain the Witt algebra of conformal transformations of the time line and appear in non-equilibrium statistical physics and in non-relativistic conformal field theory. We describe all quasi-derivations of the original and the twisted Schrödinger--Witt algebras. We prove that every quasi-derivation is the sum of a derivation, a trivial $\\frac12$-derivation, a linear map with values in the center, and a finite linear combination of maps from three new families of quasi-derivations. As corollaries, we describe all $δ$-derivations, all $δ$-biderivations and all transposed $δ$-Poisson structures of the Schrödinger--Witt algebras. Finally, we prove that every quasi-derivation of the (original or twisted) extended Schrödinger--Witt algebra is the sum of an inner derivation and a multiple of the identity map. As a consequence, there are no nontrivial $δ$-derivations (for $δ\\notin \\{\\frac12,1\\}$), $δ$-biderivations (for $δ\\neq1$), and transposed $δ$-Poisson structures on these algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23382",
  "author_total": 3,
  "authors": [
    {
      "name": "Ivan Kaygorodov"
    },
    {
      "name": "Abror Khudoyberdiyev"
    },
    {
      "name": "Zarina Shermatova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d5b06hhhcjdtm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23382",
  "fulltext_url": null,
  "id": "d5b06hhhcjdtm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23382",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7222935126",
  "pdf_url": "https://arxiv.org/pdf/2610.23382",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d5b06hhhcjdtm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23382"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quasi-derivations of the (extended) Schrödinger--Witt algebras",
  "title_text": "Quasi-derivations of the (extended) Schrödinger--Witt algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/d5b06hhhcjdtm",
  "venue": "arXiv",
  "versions": []
}