{
  "annotation_id": "ed793fb8-34be-41ad-8b62-11c4c6093b31",
  "date_created": "2026-02-17T05:53:16.075000Z",
  "date_modified": "2026-02-17T05:53:16.075000Z",
  "file_hash": "6b4ff4b99dc606c4e6ba40e18be5be2ce70186b7bde516bd38a35d50ac21c4ac",
  "private": false,
  "record": {
    "abstract": "Let $A$ be an associative algebra with a superinvolution $*$ over a field of characteristic zero, and let $c_n^*(A)$, $n = 1, 2, \\ldots$, denote its sequence of $*$-codimensions. It is well known that this sequence is either polynomially bounded or grows exponentially. In the polynomial case, a central problem in PI-theory is the classification of varieties ${V}$ for which $c_n^*({V}) \\approx \\alpha n^k$ for a given $k$. One of the main objectives of this paper is to classify minimal varieties of unitary algebras endowed with a superinvolution that exhibit quadratic codimension growth. We obtain a structural characterization, up to PI-equivalence, of all unitary algebras with quadratic codimension growth. As a consequence, we show that any unitary variety of quadratic codimension growth is generated by a direct sum of algebras generating minimal varieties.",
    "arxiv_id": "2601.08092",
    "authors": [
      "Wesley Quaresma Cota",
      "Luiz Henrique de Souza Matos"
    ],
    "categories": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Quadratic codimension growth and minimal varieties of unitary algebras with superinvolution",
    "url": "https://arxiv.org/abs/2601.08092",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1002aec3-f65a-49d9-8f78-08cb3d6d661a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}