{
  "annotation_id": "5c5d1f78-9ee7-4cee-98b6-ffac52f5d88a",
  "date_created": "2026-03-02T18:01:27.860000Z",
  "date_modified": "2026-03-02T18:01:27.860000Z",
  "file_hash": "8ed915af26d7fcf2af7a05ba3a989a793c6ac9e8958d348fe810819e904bf7f1",
  "private": false,
  "record": {
    "abstract": "Properties of metrics and pairs consisting of left and right connections are\nstudied on the bimodules of differential 1-forms. Those bimodules are obtained\nfrom the derivation based calculus of an algebra of matrix valued functions,\nand an $SL\\sb q(2,\\IC)$-covariant calculus of the quantum plane plane at a\ngeneric $q$ and the cubic root of unity. It is shown that, in the\naforementioned examples, giving up the middle-linearity of metrics\nsignificantly enlarges the space of metrics. A~metric compatibility condition\nfor the pairs of left and right connections is defined. Also, a compatibility\ncondition between a left and right connection is discussed. Consequences\nentailed by reducing to the centre of a bimodule the domain of those conditions\nare investigated in detail. Alternative ways of relating left and right\nconnections are considered.",
    "arxiv_id": "q-alg/9602035",
    "authors": [
      "L. Dcabrowski",
      "P. M. Hajac",
      "G. Landi",
      "P. Siniscalco"
    ],
    "categories": [
      "q-alg",
      "gr-qc",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "doi": "10.1063/1.531644",
    "journal_ref": "J.Math.Phys. 37 (1996) 4635-4646",
    "title": "Metrics and Pairs of Left and Right Connections on Bimodules",
    "url": "https://arxiv.org/abs/q-alg/9602035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cae70b6b-d60b-46c0-9e08-50d1a0b5d343",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}