{
  "abstract": "We introduce and study completeness for multiplicative $n$-ary Hom-Nambu superalgebras. Because an $n$-ary Hom-Nambu bracket is not necessarily totally super-skew-symmetric, we define its center as the intersection of its positional centers. A multiplicative $n$-ary Hom-Nambu superalgebra is complete when its center is trivial, and every $α^{k+1}$-derivation is inner for all $k \\geq 0$. We show that this notion reduces to the usual completeness for multiplicative $n$-Hom-Lie superalgebras. Furthermore, we establish a completeness criterion for surjective brackets with a zero twisting map and provide a complete $n$-ary Hom-Nambu superalgebra that is not an $n$-Hom-Lie superalgebra. We also study the direct sums of complete $n$-Hom-Lie superalgebras and the behavior of centers under twisting. Finally, starting from a multiplicative Hom-Lie superalgebra, we consider recursively induced multiplicative $n$-ary Hom-Nambu superalgebras. When the twisting map is surjective, we prove that triviality of the center is preserved and reflected in this construction. We also observe that every binary $α^k$-derivation satisfies the corresponding relative $α^k$-derivation identity for the induced bracket. Finally, we determine the complete members in the selected low-dimensional Hom-Lie and $3$-Hom-Lie superalgebra classifications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30182",
  "author_total": 3,
  "authors": [
    {
      "name": "Mohammad Reza Farhangdoost"
    },
    {
      "name": "Mohammad Reza Hafezi"
    },
    {
      "name": "Sergei Silvestrov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dg97w72n58ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30182",
  "fulltext_url": null,
  "id": "1dg97w72n58ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30182",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7204946119",
  "pdf_url": "https://arxiv.org/pdf/2608.30182",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dg97w72n58ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30182",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30182"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Completeness of $n$-ary Hom-Nambu and Hom-Lie Superalgebras",
  "title_text": "On Completeness of n-ary Hom-Nambu and Hom-Lie Superalgebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1dg97w72n58ca",
  "venue": "arXiv",
  "versions": []
}