{
  "abstract": "The finite-dimensional $F$-algebras $D=F(e_{11}+e_{33})+Fe_{22}+Fe_{12}+Fe_{13}+Fe_{23} \\subseteq UT_3$ and $D_0=Fe_{22}+Fe_{33}+Fe_{12}+Fe_{13}+Fe_{14}+Fe_{23}+Fe_{24}+Fe_{34} \\subseteq UT_4$ occupy a distinguished position in the theory of central polynomials. Together with the infinite-dimensional Grassmann algebra, these algebras generate the only varieties of almost polynomial growth of proper central codimensions. We determine finite generating sets for their $T$-spaces of central polynomials and compute their central and proper central codimensions. We also prove that every group grading on $D_0$ is isomorphic to an elementary grading and determine the identities and codimensions associated with all its $\\mathbb{Z}_2$-gradings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17408",
  "author_total": 2,
  "authors": [
    {
      "name": "Wesley Quaresma Cota"
    },
    {
      "name": "Daniela Martinez Correa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/984ckg3bwf98q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17408",
  "fulltext_url": null,
  "id": "984ckg3bwf98q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17408",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221801956",
  "pdf_url": "https://arxiv.org/pdf/2610.17408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/984ckg3bwf98q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Group gradings, graded identities and central polynomials of algebras with almost polynomial $δ$-growth",
  "title_text": "Group gradings, graded identities and central polynomials of algebras with almost polynomial δ-growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/984ckg3bwf98q",
  "venue": "arXiv",
  "versions": []
}