{
  "id": "1812.08528",
  "version": "v1",
  "published": "2018-12-20T12:48:54.000Z",
  "updated": "2018-12-20T12:48:54.000Z",
  "title": "Lie algebras of topological quivers",
  "authors": [
    "Andrea Appel",
    "Francesco Sala",
    "Olivier Schiffmann"
  ],
  "comment": "36 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce a new class of infinite-dimensional Lie algebras, which do not fall into the realm of Kac-Moody algebras (or their generalizations by Borcherds and Bozec) but arise as continuum colimits of Borcherds-Kac-Moody algebras. They are associated with a topological generalization of the notion of quiver, where vertices are replaced by intervals in a one-dimensional topological space. They display certain exotic features such as a Cartan subalgebra of uncountable dimension, a continuum root system with no simple roots, and they are presented by exclusively quadratic Serre relations. For these Lie algebras, we prove an analogue of the Gabber-Kac-Serre theorem, providing a complete set of defining relations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-20T12:48:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological quivers",
      "infinite-dimensional lie algebras",
      "continuum root system",
      "exclusively quadratic serre relations",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}