{
  "annotation_id": "b198d537-d919-4d57-91ab-a0277461ea90",
  "date_created": "2026-02-17T05:53:20.290000Z",
  "date_modified": "2026-02-17T05:53:20.290000Z",
  "file_hash": "208dfd4c9f2a74d3836d242a3a51294e70ef5dd4fef335c454bdbf08dc25c205",
  "private": false,
  "record": {
    "abstract": "For an associative algebra $A$ over a field of characteristic zero, let $P_n(A)$ and $P_n^z(A)$ denote the spaces of multilinear polynomials of degree $n$ modulo the polynomial identities and the central polynomials of $A$, respectively. We also write $\\Delta_n(A)$ for the space of multilinear central polynomials of degree $n$ modulo the polynomial identities of $A$. The corresponding sequences of colengths, central colengths and proper central colengths measure the number of irreducible components in the $S_n$-module decompositions of $P_n(A)$, $P_n^z(A)$ and $\\Delta_n(A)$, respectively. In this paper, we investigate several examples of PI-algebras and explicitly describe their cocharacter, central cocharacter and proper central cocharacter sequences. As a consequence, we obtain a complete classification, up to PI-equivalence, of all algebras whose sequences of colengths and central colengths are bounded by a constant.",
    "arxiv_id": "2601.09546",
    "authors": [
      "Wesley Quaresma Cota",
      "Thais Silva do Nascimento"
    ],
    "categories": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On the multiplicities of the central cocharacter of algebras with polynomial identities",
    "url": "https://arxiv.org/abs/2601.09546",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5c4c9eca-eceb-42ec-a4dd-e65b0257ee52",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}