{
  "abstract": "We study local derivations and local automorphisms of finite-dimensional nilpotent complex Lie and right Leibniz algebras. We prove that every non-abelian Lie algebra in this class admits both a local derivation which is not a derivation and a local automorphism which is not an automorphism. The constructions use a derivation $D$ satisfying $0\\ne D([L,L])\\subseteq Z(L)$. For non-abelian right Leibniz algebras, both existence statements hold whenever the dimension is at most seven or the nilpotency class is at most four. We construct an eight-dimensional non-Lie algebra of class five satisfying $\\LocDer(A)=\\Der(A)$ and $\\LocAut(A)=\\Aut(A)$. Consequently, eight and five are the least possible dimension and nilpotency class, respectively, for either equality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40348",
  "author_total": 3,
  "authors": [
    {
      "name": "Khusainboy Atajonov"
    },
    {
      "name": "Abror Khudoyberdiyev"
    },
    {
      "name": "Bakhtiyor Yusupov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86h7bebqby4ye.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40348",
  "fulltext_url": null,
  "id": "86h7bebqby4ye",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40348",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86h7bebqby4ye.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40348"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local Derivations and Local Automorphisms of Arbitrary Finite-Dimensional Nilpotent Lie and Leibniz Algebras",
  "title_text": "Local Derivations and Local Automorphisms of Arbitrary Finite-Dimensional Nilpotent Lie and Leibniz Algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/86h7bebqby4ye",
  "venue": "arXiv",
  "versions": []
}