{
  "id": "1405.6441",
  "version": "v4",
  "published": "2014-05-26T00:42:45.000Z",
  "updated": "2014-11-18T12:48:13.000Z",
  "title": "Affine cellularity of BLN-algebras",
  "authors": [
    "Weideng Cui"
  ],
  "comment": "We add the idempotence of affine cell ideals inspired by Nakajima, which implies that BLN-algebras have finite global dimension. Thanks to the referees' pertinent suggestions, I re-write the whole manu in my own way according to my understanding, and I am very sorry for my previous mistakes!",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We show that the BLN-algebra, which was introduced by McGerty, is affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals are generated by idempotents. This particularly implies that the global dimension of BLN-algebras is finite. For affine type $A$, thus we obtain that the affine $q$-Schur algebra $\\mathfrak{U}_{D,n,n},$ when $D< n,$ is affine cellular and has finite global dimension.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-15T13:47:09.000Z",
      "abstract": "We show that the BLN-algebras, which are introduced by McGerty, are affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals are generated by idempotents. This particularly implies that the global dimension of BLN-algebras is finite. For affine $A$ type, thus we obtain that the affine $q$-Schur algebras $\\mathfrak{U}_{D,n,n},$ when $D< n,$ are affine cellular and have finite global dimension.",
      "comment": "We add the idempotence of affine cell ideals inspired by Nakajima, which implies that BLN-algebras have finite global dimension. We also show that BLN-algebras and affine $q$-Schur algebras $\\mathfrak{U}_{D,n,n},$ when $D< n,$ are affine quasi-hereditary algebras. arXiv admin note: text overlap with arXiv:math/0212253, arXiv:1011.2010 by other authors",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-11-18T12:48:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine cellularity",
      "bln-algebras",
      "finite global dimension",
      "affine cell ideals",
      "stronger property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6441C"
    }
  }
}