{
  "abstract": "Let $F$ be a field of characteristic zero and consider $M_2(F),$ the algebra of $2\\times 2$ matrices over $F,$ with canonical $\\mathbb{Z}_2$-grading and endowed with transpose superinvolution. In this paper, we present the generators of the $T_2^*$-ideal of $*$-identities and of the $T_2^*$-subspace of central $*$-polynomials of $M_2(F).$ As a consequence, we determine the sequences of $*$-codimensions and $\\langle n\\rangle$-cocharacters of $M_2(F)$. In particular, we prove that the $n$-th $*$-codimension grows like $4^nn^{-1/2}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20458",
  "author_total": 2,
  "authors": [
    {
      "name": "Rafael Bezerra dos Santos"
    },
    {
      "name": "Lucas Reis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ep443wksx5718.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20458",
  "fulltext_url": null,
  "id": "ep443wksx5718",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20458",
  "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": "W7213583182",
  "pdf_url": "https://arxiv.org/pdf/2609.20458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ep443wksx5718.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20458"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with transpose superinvolution",
  "title_text": "Polynomial identities, central polynomials and cocharacters of M_2(F) with transpose superinvolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/ep443wksx5718",
  "venue": "arXiv",
  "versions": []
}