{
  "id": "2210.12351",
  "version": "v1",
  "published": "2022-10-22T04:47:16.000Z",
  "updated": "2022-10-22T04:47:16.000Z",
  "title": "Hall algebras associated to root categories",
  "authors": [
    "Haicheng Zhang"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT",
    "math.QA",
    "math.RA"
  ],
  "abstract": "Let $\\mathcal {A}$ be a finitary hereditary abelian category. We define a Hall algebra for the root category of $\\mathcal {A}$ by applying the derived Hall numbers of the bounded derived category $D^b(\\mathcal {A})$, which is proved to be isomorphic to the Drinfeld double Hall algebra of $\\mathcal {A}$. In the appendix, we also define the 1-periodic derived Hall algebra via the derived Hall numbers of $D^b(\\mathcal {A})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-22T04:47:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "root category",
      "derived hall numbers",
      "finitary hereditary abelian category",
      "drinfeld double hall algebra",
      "derived hall algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}