{
  "abstract": "Let $(P,\\cdot,d)$ be a differential perm algebra over a field of characteristic zero, i.e. an associative algebra satisfying $(ab)c=(ba)c$ and equipped with a derivation $d$. We study polynomial identities in the algebras obtained by the derived operations \\[ a\\prec b=ab',\\quad a\\succ b=a'b,\\quad a\\blacklozenge b=ab'+ba',\\quad a\\bullet b=a'b+ab',\\quad a\\Diamond b=ab'-ba',\\quad a\\circ b=a'b-ab', \\] where $a'=d(a)$. We first prove that any nontrivial differential polynomial identity that does not belong to the right annihilator of the free differential perm algebra implies a differential identity of the form $a_1'a_2'\\cdots a_m'=0$ for some positive integer $m$. We then obtain explicit generating sets and determine the dimensions of the multilinear homogeneous components of the subalgebras of the free differential perm algebra generated by $X$ with respect to the products $\\blacklozenge$ and $\\bullet$. Finally, we construct perm-Witt type Lie and Leibniz algebras arising naturally from differential perm algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00139",
  "author_total": 2,
  "authors": [
    {
      "name": "F. A. Mashurov"
    },
    {
      "name": "B. K. Sartayev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8efx5f31a3yfz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00139",
  "fulltext_url": null,
  "id": "8efx5f31a3yfz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00139",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2605.00139",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8efx5f31a3yfz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2605.00139",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00139"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Identities in differential perm algebras",
  "title_text": "Identities in differential perm algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/8efx5f31a3yfz",
  "venue": "arXiv",
  "versions": []
}