{
  "id": "2005.10617",
  "version": "v1",
  "published": "2020-05-21T13:09:16.000Z",
  "updated": "2020-05-21T13:09:16.000Z",
  "title": "Quantum cluster characters of Hall algebras revisited",
  "authors": [
    "Changjian Fu",
    "Liangang Peng",
    "Haicheng Zhang"
  ],
  "comment": "26 pages",
  "categories": [
    "math.RT",
    "math.QA",
    "math.RA"
  ],
  "abstract": "Let $Q$ be a finite acyclic valued quiver. We give a bialgebra structure and an integration map on the Hall algebra associated to the morphism category of projective valued representations of $Q$. As an application, we recover the surjective homomorphism defined in \\cite{DXZ}, which realizes the principal coefficient quantum cluster algebra $\\A_q(Q)$ as a sub-quotient of the Hall algebra of morphisms. Moreover, we also recover the quantum Caldero--Chapoton formula, as well as their cluster multiplication formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-21T13:09:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hall algebra",
      "quantum cluster characters",
      "principal coefficient quantum cluster algebra",
      "quantum caldero-chapoton formula",
      "finite acyclic valued quiver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}