{
  "id": "2105.05440",
  "version": "v2",
  "published": "2021-05-12T05:41:53.000Z",
  "updated": "2021-05-20T08:08:22.000Z",
  "title": "Commutativity of Quantization and Reduction for Quiver Representations",
  "authors": [
    "Hu Zhao"
  ],
  "comment": "28 pages",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP",
    "math.RA"
  ],
  "abstract": "Given a finite quiver, its double may be viewed as its non-commutative \"cotangent\" space, and hence is a non-commutative symplectic space. Crawley-Boevey, Etingof and Ginzburg constructed the non-commutative reduction of this space while Schedler constructed its quantization. We show that the non-commutative quantization and reduction commute with each other. Via the quantum and classical trace maps, such a commutativity induces the commutativity of the quantization and reduction on the space of quiver representations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-05-20T08:08:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "53D55",
      "81R60"
    ],
    "keywords": [
      "quiver representations",
      "non-commutative symplectic space",
      "finite quiver",
      "reduction commute",
      "classical trace maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}