{
  "abstract": "For a fixed positive real constant $m$, a real Lie algebra of even dimension $2k$ admits a nonzero left-invariant $m$-modified conformal vector field for some nondegenerate metric if and only if an adjoint operator has a nonzero real eigenvalue. In that case, a solution exists with neutral signature $(k,k)$ and zero conformal factor. As an application, we classify the admissible four-dimensional Lie algebras and metric signatures; the only Lorentzian exceptions among the admissible algebras are $\\mathfrak{aff}(\\mathbb{C})$ and the diamond algebra. On a pseudo-Riemannian manifold of arbitrary indefinite signature, a nonzero $m$-modified conformal vector field forces lightlike geodesic incompleteness, even when its conformal factor is variable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22759",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhigang Li"
    },
    {
      "name": "Shaoqiang Deng"
    },
    {
      "name": "Hui Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0b4xhmq5d44k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22759",
  "fulltext_url": null,
  "id": "b0b4xhmq5d44k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22759",
  "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.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7222968017",
  "pdf_url": "https://arxiv.org/pdf/2610.22759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0b4xhmq5d44k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An Adjoint Criterion for Left-Invariant $m$-Modified Conformal Vector Fields on Even-Dimensional Lie Groups",
  "title_text": "An Adjoint Criterion for Left-Invariant m-Modified Conformal Vector Fields on Even-Dimensional Lie Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/b0b4xhmq5d44k",
  "venue": "arXiv",
  "versions": []
}