{
  "annotation_id": "077a6b31-5048-454f-ae43-109a290b69c4",
  "date_created": "2026-03-02T18:01:28.013000Z",
  "date_modified": "2026-03-02T18:01:28.013000Z",
  "file_hash": "aa9669f3a7ee5d45e1da392d55586c00ab74e8fbdddc8b191e414a382dd76809",
  "private": false,
  "record": {
    "abstract": "An infinite dimensional algebra which is a non-decomposable reducible\nrepresentation of $su(2)$ is given. This algebra is defined with respect to two\nreal parameters. If one of these parameters is zero the algebra is the\ncommutative algebra of functions on the sphere, otherwise it is a\nnoncommutative analogue. This is an extension of the algebra normally refered\nto as the (Berezin) quantum sphere or ``fuzzy\u0027\u0027 sphere. A natural indefinite\n``inner\u0027\u0027 product and a basis of the algebra orthogonal with respect to it are\ngiven. The basis elements are homogenious polynomials, eigenvectors of a\nLaplacian, and related to the Hahn polynomials. It is shown that these elements\ntend to the spherical harmonics for the sphere. A Moyal bracket is constructed\nand shown to be the standard Moyal bracket for the sphere.",
    "arxiv_id": "q-alg/9703038",
    "authors": [
      "J. Gratus"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1063/1.532003",
    "title": "A Natural Basis of States for the Noncommutative Sphere and its Moyal   bracket",
    "url": "https://arxiv.org/abs/q-alg/9703038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c20bfa04-fd60-427c-a4cc-5215d7587698",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}