{
  "id": "1210.6542",
  "version": "v1",
  "published": "2012-10-24T14:23:40.000Z",
  "updated": "2012-10-24T14:23:40.000Z",
  "title": "Affine Cellularity of Khovanov-Lauda-Rouquier algebras in type A",
  "authors": [
    "Alexander S. Kleshchev",
    "Joseph W. Loubert",
    "Vanessa Miemietz"
  ],
  "doi": "10.1112/jlms/jdt023",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We prove that the Khovanov-Lauda-Rouquier algebras $R_\\al$ of type $A_\\infty$ are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\\al$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_\\al$ is finite, and yields a theory of standard and reduced standard modules for $R_\\al$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-24T14:23:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "khovanov-lauda-rouquier algebras",
      "affine cellularity",
      "affine cell ideals",
      "stronger property",
      "global dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6542K"
    }
  }
}