{
  "id": "1405.6705",
  "version": "v4",
  "published": "2014-05-26T00:45:53.000Z",
  "updated": "2015-08-20T08:26:15.000Z",
  "title": "Affine cellularity of affine $q$-Schur algebras",
  "authors": [
    "Weideng Cui"
  ],
  "comment": "10 pages. arXiv admin note: substantial text overlap with arXiv:1405.6441",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We first present an axiomatic approach to proving that an algebra with a cell theory in Lusztig's sense is affine cellular in the sense of Koenig and Xi, then we will show that the affine $q$-Schur algebra $\\mathfrak{U}_{r,n,n}$ is affine cellular. We also show that $\\mathfrak{U}_{r,n,n}$ is of finite global dimension and its derived module category admits a stratification when the parameter $v\\in \\mathbb{C}^{*}$ is not a root of unity.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-15T13:50:11.000Z",
      "abstract": "We show that the affine $q$-Schur algebra $\\mathfrak{U}_{r,n,n}$, which has been defined by Lusztig, is affine cellular in the sense of Koenig and Xi. By specializing at $v=1$, we obtain the affine cellularity of the affine Schur algebra. We also show that $\\mathfrak{U}_{r,n,n}$ is of finite global dimension, its derived module category admits a stratification and is an affine quasi-hereditary algebra when the quantum parameter $v\\in \\mathbb{C}^{*}$ is not a root of unity.",
      "comment": "We also show that $\\mathfrak{U}_{r,n,n}$ is of finite global dimension, its derived module category admits a stratification and is an affine quasi-hereditary algebra when the quantum parameter $v\\in \\mathbb{C}^{*}$ is not a root of unity. arXiv admin note: substantial text overlap with arXiv:1405.6441; and text overlap with arXiv:math/0209055, arXiv:1011.2010 by other authors",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-08-20T08:26:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine cellularity",
      "affine schur algebra",
      "affine quasi-hereditary algebra",
      "derived module category admits",
      "finite global dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6705C"
    }
  }
}