{
  "abstract": "We classify 2-local derivations on the finite-dimensional conformal Galilei Lie algebras in three natural settings: the algebra without central extension, the mass central extension, and the exotic central extension. No additivity or linearity is assumed in the definition of a 2-local derivation. We prove that in every case each 2-local derivation is an ordinary derivation. For the unextended algebra, the proof combines characteristic-quotient normalization with separating vectors, invariant bilinear forms, rank-two mixed zero anchors, and a semisimple-perturbation argument for the standard module. For the mass central extension with $2\\ell\\ge3$, the residual map is first reduced to the center and then eliminated by a symplectic-anchor construction on the Heisenberg radical; a dimension argument in the centralizer of a regular semisimple element simultaneously handles singular reductive actions and the additional central shear that occurs in spatial dimension two. The endpoint $\\ell=\\tfrac12$ is the Schrödinger algebra; a self-contained symplectic-anchor proof includes all spatial dimensions, with explicit treatment of dimensions one and two. For the exotic extension, after center normalization we use conjugate middle-weight positions and an affine middle anchor to eliminate every central translate, including the one-sided middle-weight configurations. Consequently the set of 2-local derivations coincides with the derivation algebra for all admissible parameters, and hence every 2-local derivation in these families is automatically linear.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25808",
  "author_total": 2,
  "authors": [
    {
      "name": "Bekzod Sultonboyev"
    },
    {
      "name": "Bakhtiyor Yusupov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/csxdt2v1g7cjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25808",
  "fulltext_url": null,
  "id": "csxdt2v1g7cjz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25808",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7223052904",
  "pdf_url": "https://arxiv.org/pdf/2610.25808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/csxdt2v1g7cjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "2-Local Derivations on Conformal Galilei Lie Algebras and Their Central Extensions",
  "title_text": "2-Local Derivations on Conformal Galilei Lie Algebras and Their Central Extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/csxdt2v1g7cjz",
  "venue": "arXiv",
  "versions": []
}