{
  "id": "1302.1835",
  "version": "v3",
  "published": "2013-02-07T19:30:18.000Z",
  "updated": "2015-04-13T08:56:35.000Z",
  "title": "Counting using Hall Algebras II. Extensions from Quivers",
  "authors": [
    "Jiarui Fei"
  ],
  "comment": "18 pages. V2. A missing diagram added. V3. Final version to appear Algebr. Represent. Theory (2015)",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We count the $\\mathbb{F}_q$-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras -- one is one-point extended from a quiver $Q$, and the other is the Dynkin $A_2$ tensored with $Q$. For both, we obtain explicit formulas. We study when they are polynomial-count. We follow the similar line as in the first paper but algebraic manipulations in Hall algebra will be replaced by corresponding geometric constructions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-08T14:45:55.000Z",
      "abstract": "We count the $F_q$-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras -- one is one-point extended from a quiver $Q$, and the other is the Dynkin $A_2$ tensored with $Q$. For both, we obtain explicit formulas. We study when they are polynomial-count. We follow the similar line as in the first paper but algebraic manipulations in Hall algebra will be replaced by corresponding geometric constructions.",
      "comment": "A missing diagram added. Happy Snake Year!",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-13T08:56:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "14D20",
      "14N10"
    ],
    "keywords": [
      "hall algebra",
      "extensions",
      "explicit formulas",
      "quiver representations",
      "similar line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1835F"
    }
  }
}