{
  "abstract": "We study generalized derivations of complex multiplicative α2-weighted Ω-Hom-Lie superalgebras. The chosen structural identity is shown to be stable under Yau twisting, and every regular algebra in this class untwists canonically to an Ω-Lie superalgebra. To retain the auxiliary operators that occur in generalized derivation identities, we work with generalized derivation triples and quasiderivation pairs. In this framework, these derivation-type maps are treated as mathematical operators encoding infinitesimal symmetries of the underlying graded algebraic structure. The triple space is a Lie superalgebra, and quasiderivation pairs fit into a short exact sequence of Lie superalgebras whose kernel measures precisely the ambiguity of the auxiliary map. We prove GDerα(L)=QDerα(L)+QCentα(L), and establish the corresponding Ω-compatible decomposition for balanced generalized derivations. We then construct a three-layer envelope for generalized derivation triples and a two-layer envelope for quasiderivation pairs, obtaining injective Lie-superalgebra embeddings into α-commuting derivation algebras. A structural obstruction shows that, when α2≠0, the original nonzero Ω cannot simply be copied to the active layers of these two-step envelopes as their structural form. For centerless algebras, the full derivation superalgebra of the two-layer envelope is determined as an explicit semidirect product. Finally, a structure-constant criterion reduces the pair and triple spaces to homogeneous linear systems. For the regular family Hτ, τ∈C×∖{1}, we obtain dimDerατ=1 and dimQDerατ=dimGDerατ=4, while the Ω-compatible first-component space has dimension 3.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Muntasir Suhail",
      "orcid": "0009-0009-6835-4896"
    },
    {
      "affs": [
        0
      ],
      "name": "Osman Abdalla Adam Osman",
      "orcid": "0000-0001-5085-4002"
    },
    {
      "affs": [
        0
      ],
      "name": "Mohammed Rabih",
      "orcid": "0000-0002-3588-9693"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6h97spq61hcpk.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203813",
  "fulltext_url": null,
  "id": "6h97spq61hcpk",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3813",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7222993529",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/6h97spq61hcpk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203813",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Advanced Topics in Algebra",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Generalized Derivations and Canonical Envelopes of Complex α2-Weighted Ω-Hom-Lie Superalgebras",
  "title_text": "Generalized Derivations and Canonical Envelopes of Complex α2-Weighted Ω-Hom-Lie Superalgebras",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/6h97spq61hcpk",
  "venue": "Mathematics",
  "versions": []
}