{
  "id": "1409.1195",
  "version": "v1",
  "published": "2014-09-03T18:51:31.000Z",
  "updated": "2014-09-03T18:51:31.000Z",
  "title": "A KLR Grading of the Brauer Algebras",
  "authors": [
    "Ge Li"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct a naturally $\\mathbb Z$-graded algebra $\\mathscr G_n(\\delta)$ over $R$ with KLR-like relations and give an explicit isomorphism between $\\mathscr G_n(\\delta)$ and $\\mathscr B_n(\\delta)$, the Brauer algebras over $R$, when $R$ is a field of characteristic $0$. This isomorphism allows us to exhibit a non-trivial $\\mathbb Z$-grading on the Brauer algebras over a field of characteristic $0$. As a byproduct of the proof, we also construct an explicit homogeneous cellular basis for $\\mathscr G_n(\\delta)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-03T18:51:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brauer algebras",
      "klr grading",
      "explicit homogeneous cellular basis",
      "explicit isomorphism",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1195L"
    }
  }
}