{
  "annotation_id": "1d4fa7a5-387e-4f1d-8ae5-93e485611d69",
  "date_created": "2026-03-02T18:01:21.579000Z",
  "date_modified": "2026-03-02T18:01:21.579000Z",
  "file_hash": "30db3ff0c74815809e6b5d5047edfc77754da2fad0476826bf7f6c7d5f48fefd",
  "private": false,
  "record": {
    "abstract": "The forms of the invariant primitive tensors for the simple Lie algebras A_l,\nB_l, C_l and D_l are investigated. A new family of symmetric invariant tensors\nis introduced using the non-trivial cocycles for the Lie algebra cohomology.\nFor the A_l algebra it is explicitly shown that the generic forms of these\ntensors become zero except for the l primitive ones and that they give rise to\nthe l primitive Casimir operators. Some recurrence and duality relations are\ngiven for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3)\nand su(4) are also provided. Finally, new relations involving the d and f su(n)\ntensors are given.",
    "arxiv_id": "physics/9706006",
    "authors": [
      "J. A. de Azcarraga",
      "A. J. Macfarlane",
      "A. J. Mountain",
      "J. C. Perez Bueno"
    ],
    "categories": [
      "math-ph",
      "hep-th",
      "math.MP",
      "math.QA",
      "q-alg"
    ],
    "doi": "10.1016/S0550-3213(97)00609-3",
    "journal_ref": "Nucl.Phys. B510 (1998) 657-687",
    "title": "Invariant tensors for simple groups",
    "url": "https://arxiv.org/abs/physics/9706006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e99e5517-974d-4ec4-b3ed-6edfdb209d4e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}