{
  "abstract": "We compute the homogeneous derivations and the homogeneous quasi-derivations of the Block Lie superalgebras $S(q)$, whose even part is the Block Lie algebra $\\mathcal{B}(q)$. For every $q\\in\\mathbb C$, the space $\\mathfrak{Der}_θ(S(q))$ is the direct sum of the inner derivations and an explicitly given finite-dimensional space of outer derivations; in particular, for $q\\neq0$ a new odd outer derivation appears if and only if $q\\in2\\mathbb Z^*$. For $q\\in\\mathbb C^*$ we prove that $\\mathfrak{QDer}(S(q))=\\mathfrak{Der}(S(q))\\oplus\\langle \\id\\rangle$ if $q\\notin\\mathbb Z$, and that for $q\\in\\mathbb Z^{*}$ the superalgebra $S(q)$ has an infinite-dimensional space of nontrivial quasi-derivations, namely all graded linear maps with values in the center. For $q=0$ we also describe all homogeneous quasi-derivations: modulo maps with values in the center, they are spanned by $\\id$, three further maps and infinite families of maps shifting the $\\mathbb Z^2$-grading; in particular, $\\mathfrak{QDer}(S(0))/\\mathfrak{Der}(S(0))$ is infinite-dimensional. As corollaries, we obtain the complete description of homogeneous $δ$-derivations of $S(q)$, $q\\neq0$, and prove that, in contrast with the Block Lie algebras $\\mathcal{B}(q)$, the superalgebras $S(q)$, $q\\neq0$, do not admit nontrivial transposed $δ$-Poisson superalgebra structures for any $δ\\notin\\{0,1\\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23150",
  "author_total": 3,
  "authors": [
    {
      "name": "Ivan Kaygorodov"
    },
    {
      "name": "Abror Khudoyberdiyev"
    },
    {
      "name": "Zarina Shermatova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0sx9ry2d9y87.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23150",
  "fulltext_url": null,
  "id": "f0sx9ry2d9y87",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23150",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7222973057",
  "pdf_url": "https://arxiv.org/pdf/2610.23150",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0sx9ry2d9y87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23150",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23150"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Derivations and quasi-derivations of Block Lie superalgebras $S(q)$",
  "title_text": "Derivations and quasi-derivations of Block Lie superalgebras S(q)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/f0sx9ry2d9y87",
  "venue": "arXiv",
  "versions": []
}