{
  "id": "math/0502409",
  "version": "v1",
  "published": "2005-02-19T01:02:41.000Z",
  "updated": "2005-02-19T01:02:41.000Z",
  "title": "An application of free Lie algebras to current algebras and their representation theory",
  "authors": [
    "Vyjayanthi Chari",
    "Jacob Greenstein"
  ],
  "comment": "15 pages",
  "journal": "Contemp. Math., 392 (2005), 15-31",
  "categories": [
    "math.RT"
  ],
  "abstract": "We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current alg ebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representation of the current algebra. These representations include certain well-known families of representations of the current algebra of a simple Lie algebra. Another family of examples, which are the classical limits of the Kirillov-Reshe tikhin modules, are also obtained explicitly by using a construction of Kostant. Finally we study extensi ons in the category of finite dimensional modules of the current algebra of a simple Lie algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-19T01:02:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16B67"
    ],
    "keywords": [
      "current algebra",
      "free lie algebra",
      "representation theory",
      "simple lie algebra",
      "kac-moody algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2409C"
    }
  }
}