{
  "id": "1706.03889",
  "version": "v1",
  "published": "2017-06-13T02:13:01.000Z",
  "updated": "2017-06-13T02:13:01.000Z",
  "title": "On the module structure of the center of hyperelliptic Krichever-Novikov algebras",
  "authors": [
    "Ben Cox",
    "Mee Seong Im"
  ],
  "comment": "32 pages, submitted",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the coordinate ring $R := R_{2}(p)=\\mathbb{C}[t^{\\pm 1}, u : u^2 = t(t-\\alpha_1)\\cdots (t-\\alpha_{2n})] $ of a hyperelliptic curve and let $\\mathfrak{g}\\otimes R$ be the corresponding current Lie algebra where $\\mathfrak g$ is a finite dimensional simple Lie algebra defined over $\\mathbb C$. We give a generator and relations description of the universal central extension of $\\mathfrak{g}\\otimes R$ in terms of certain families of polynomials $P_{k,i}$ and $Q_{k,i}$ and describe how the center of $\\Omega_R/dR$ decomposes into a direct sum of irreducible representations when the automorphism group is $C_{2k}$ or $D_{2k}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T02:13:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperelliptic krichever-novikov algebras",
      "module structure",
      "finite dimensional simple lie algebra",
      "corresponding current lie algebra",
      "universal central extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}