{
  "annotation_id": "fb86bad5-8f85-4c96-93c4-70e8eb07757e",
  "date_created": "2026-02-17T05:53:15.284000Z",
  "date_modified": "2026-02-17T05:53:15.284000Z",
  "file_hash": "37bcd824eb0cf5939a09c4d5bcbc1a973194efaa9dd113bde655f5b4a43b8d8c",
  "private": false,
  "record": {
    "abstract": "Nilpotent evolution algebras of maximal nilindex admit a natural basis in which the structure matrix is strictly upper triangular. In this paper we classify Rota{Baxter operators of weights zero and one on such algebras. We prove that every Rota{Baxter operator is upper triangular with respect to a natural basis. For weight zero, a strong rigidity phenomenon occurs: the operators are diagonal up to possible perturbations supported in the last basis vector. For weight one, a richer structure appears, including both triangular and non-triangular families, with the diagonal entries governed by a rational recurrence relation. Our results provide a complete description of Rota{Baxter operators on nilpotent evolution algebras of maximal nilindex.",
    "arxiv_id": "2601.08669",
    "authors": [
      "Izzat Qaralleh",
      "Farrukh Mukhamedov",
      "Otabek Khakimov"
    ],
    "categories": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Rota-Baxter operators of nilpotent evolution algebras with maximal nilindex",
    "url": "https://arxiv.org/abs/2601.08669",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2bd6e916-6a11-4dcd-8cc2-097b47fa2c49",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}