{
  "abstract": "Commuting graphs of Okubo algebras are considered, and the problem of their connectivity is studied. The commuting graph of a pseudo-octonion algebra $P_8(\\mathbb{F})$ over a field $\\mathbb{F}$, $\\mathrm{char} \\, \\mathbb{F} \\neq 3$, that contains a primitive cubic root of unity is shown to be isomorphic to the commuting graph of the matrix algebra $M_3(\\mathbb{F})$. As a consequence, if the field $\\mathbb{F}$ is algebraically closed, then the diameter of the commuting graph for the unique Okubo algebra over $\\mathbb{F}$ equals $4$. It is shown that the commuting graph of the real division Okubo algebra is connected, and its diameter also equals $4$. The proof of this result relies on the fact that, given any two idempotents in an arbitrary Okubo algebra, the intersection of their centralizers is always nonzero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: S. Zhilina, D. Pavlinov, Commuting graphs of Okubo algebras, J. Math. Sci. 299(6) (2026) 938-950",
  "arxiv": "2608.28006",
  "author_total": 2,
  "authors": [
    {
      "name": "Svetlana Zhilina"
    },
    {
      "name": "Danil Pavlinov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8fwr2epycqbw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28006",
  "fulltext_url": null,
  "id": "f8fwr2epycqbw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28006",
  "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.RA"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.28006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8fwr2epycqbw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28006"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Commuting graphs of Okubo algebras",
  "title_text": "Commuting graphs of Okubo algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/f8fwr2epycqbw",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s10958-026-08484-2",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}