{
  "abstract": "We develop the method of central extensions (the Skjelbred--Sund method) for nilpotent right alternative algebras over the field of complex numbers and apply it to obtain the algebraic classification of five-dimensional nilpotent right alternative algebras. More precisely, we classify, up to isomorphism, all complex five-dimensional nilpotent right alternative algebras that have no annihilator component (that is, which are not a direct sum of a smaller algebra and a one-dimensional algebra with zero product) and which are not $2$-step nilpotent. Every such algebra is a non-split central extension of a nontrivial nilpotent right alternative algebra of dimension three (by a two-dimensional space) or of dimension four (by a one-dimensional space). For each of the relevant three- and four-dimensional algebras we compute the second cohomology space, the automorphism group and its action on the second cohomology, and we determine all orbits that give non-split extensions. The resulting list consists of $124$ algebras and families of algebras; it contains $29$ algebras with two-dimensional annihilator and $95$ algebras with one-dimensional annihilator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09816",
  "author_total": 2,
  "authors": [
    {
      "name": "Zohida Raxmatova"
    },
    {
      "name": "Aloberdi Sattarov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2qa69d3zsbvd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09816",
  "fulltext_url": null,
  "id": "d2qa69d3zsbvd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09816",
  "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"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7220994386",
  "pdf_url": "https://arxiv.org/pdf/2610.09816",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2qa69d3zsbvd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09816",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09816"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The algebraic classification of five-dimensional nilpotent right alternative algebras",
  "title_text": "The algebraic classification of five-dimensional nilpotent right alternative algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/d2qa69d3zsbvd",
  "venue": "arXiv",
  "versions": []
}