{
  "id": "2410.16056",
  "version": "v1",
  "published": "2024-10-21T14:35:58.000Z",
  "updated": "2024-10-21T14:35:58.000Z",
  "title": "Quantizations of transposed Poisson algebras by Novikov deformations",
  "authors": [
    "Siyuan Chen",
    "Chengming Bai"
  ],
  "comment": "14 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "math.RA"
  ],
  "abstract": "The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subclass of transposed Poisson algebras, and hence the Novikov deformation is defined to be the quantization of the corresponding transposed Poisson algebra. As a direct consequence, we revisit the relationship between transposed Poisson algebras and Novikov-Poisson algebras due to the fact that there is a natural Novikov deformation of the commutative associative algebra in a Novikov-Poisson algebra. Hence all transposed Poisson algebras of Novikov-Poisson type, including unital transposed Poisson algebras, can be quantized. Finally, we classify the quantizations of $2$-dimensional complex transposed Poisson algebras in which the Lie brackets are non-abelian up to equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-21T14:35:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D10",
      "13N15",
      "17A30",
      "17B63",
      "53D55"
    ],
    "keywords": [
      "quantization",
      "commutative associative algebra",
      "dimensional complex transposed poisson algebras",
      "novikov-poisson algebra",
      "natural novikov deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}