{
  "abstract": "Given a finite dimensional Lie algebra $L$ on a finite field $\\mathbb{F}_{p^n}$ of prime power order $p^n$ (with $n$ positive integer and $p$ prime), we consider the number of modular pairs $(A,B)$ in the lattice of all subalgebras $\\mathcal{L}(L)$ and introduce the notion of ``subalgebra commutativity degree'' of $L$. This represents the probability to find that two randomly chosen subalgebras $A$ and $B$ of $L$ are permutable. We investigate the subalgebra commutativity degree of $L$ in connection with recent techniques of algebraic combinatorics and number theory, providing upper and lower bounds which may influence the structure of $L$. A specific study for the subalgebra commutativity degree of Heisenberg algebras is executed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19086",
  "author_total": 3,
  "authors": [
    {
      "name": "Seid Kassaw Muhie"
    },
    {
      "name": "Daniele Ettore Otera"
    },
    {
      "name": "Francesco G. Russo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32swh7d089n9k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19086",
  "fulltext_url": null,
  "id": "32swh7d089n9k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19086",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213501185",
  "pdf_url": "https://arxiv.org/pdf/2609.19086",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32swh7d089n9k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.19086",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the number of modular pairs in finite dimensional Lie algebras on finite fields",
  "title_text": "On the number of modular pairs in finite dimensional Lie algebras on finite fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/32swh7d089n9k",
  "venue": "arXiv",
  "versions": []
}