{
  "id": "1202.1622",
  "version": "v2",
  "published": "2012-02-08T08:27:13.000Z",
  "updated": "2012-10-22T11:56:48.000Z",
  "title": "Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data",
  "authors": [
    "Seok-Jin Kang",
    "Masaki Kashiwara",
    "Euiyong Park"
  ],
  "comment": "We revise a few typos, and update references",
  "doi": "10.1112/plms/pds095",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We construct a geometric realization of the Khovanov-Lauda-Rouquier algebra $R$ associated with a symmetric Borcherds-Cartan matrix $A=(a_{ij})_{i,j\\in I}$ via quiver varieties. As an application, if $a_{ii} \\ne 0$ for any $i\\in I$, we prove that there exists a 1-1 correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of $U_\\A^-(\\g)$ (resp.\\ $V_\\A(\\lambda)$) and the set of isomorphism classes of indecomposable projective graded modules over $R$ (resp.\\ $R^\\lambda$).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-22T11:56:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric realization",
      "khovanov-lauda-rouquier algebras",
      "borcherds-cartan data",
      "kashiwaras lower global basis",
      "symmetric borcherds-cartan matrix"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.1622K"
    }
  }
}