{
  "annotation_id": "b3baca11-3b7a-4f91-aad3-81b84f0509ba",
  "date_created": "2026-03-02T18:01:28.352000Z",
  "date_modified": "2026-03-02T18:01:28.352000Z",
  "file_hash": "e3efe4a39255f284ae8202f86d2f40c57f6d16b1b716e0756dbe378a2efa1657",
  "private": false,
  "record": {
    "abstract": "Let $P(N,V)$ denote the vector space of polynomials of maximal degree less\nthan or equal to $N$ in $V$ independent variables. This space is preserved by\nthe enveloping algebra generated by a set of linear, differential operators\nrepresenting the Lie algebra $gl(V+1)$. We establish the counterpart of this\nproperty for the vector space $P(M,V) \\oplus P(N,V)$ for any values of the\nintegers $M,N,V$. We show that the operators preserving $P(M,V) \\oplus P(N,V)$\ngenerate an abstract superalgebra (non linear if $\\Delta=\\mid M-N\\mid\\geq 2$).\nA family of algebras is also constructed, extending this particular algebra by\n$\\Delta -1$ arbitrary complex parameters.",
    "arxiv_id": "q-alg/9701016",
    "authors": [
      "Yves Brihaye",
      "Jean Nuyts"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1007/s002200050430",
    "title": "The hidden symmetry algebras of a class of quasi-exactly solvable multi   dimensional operators",
    "url": "https://arxiv.org/abs/q-alg/9701016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c2f12c37-2fac-4552-a5f0-77a13c717508",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}