{
  "id": "0805.3018",
  "version": "v2",
  "published": "2008-05-20T07:35:46.000Z",
  "updated": "2017-07-14T17:12:25.000Z",
  "title": "Hyperbolic Weyl groups and the four normed division algebras",
  "authors": [
    "Alex J. Feingold",
    "Axel Kleinschmidt",
    "Hermann Nicolai"
  ],
  "comment": "56 pages, 21 figures. Revised to: (1) Correct typo in formula (4.33), (2) Correct error in Prop. 15, (3) Add references [44] and [45], (4) Match other corrections in the published version",
  "journal": "J.Algebra 322:1295-1339 (2009)",
  "doi": "10.1016/j.jalgebra.2009.05.006",
  "categories": [
    "math.RT",
    "hep-th",
    "math.GR"
  ],
  "abstract": "We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of the division algebras and associated discrete matrix groups. Our findings can be summarized by saying that the even subgroups, W^+, of the Kac-Moody Weyl groups, W, are isomorphic to generalized modular groups over K for the simply laced algebras, and to certain finite extensions thereof for the non-simply laced algebras. This hints at an extended theory of modular forms and functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-20T07:35:46.000Z",
      "comment": "56 pages, 21 figures",
      "journal": "J.Algebra 322:1295-1339,2009"
    },
    {
      "version": "v2",
      "updated": "2017-07-14T17:12:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17A35",
      "17B67",
      "20F55",
      "11F06"
    ],
    "keywords": [
      "normed division algebras",
      "hyperbolic weyl groups",
      "hyperbolic kac-moody algebras",
      "associated discrete matrix groups",
      "kac-moody weyl groups"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 789041,
      "adsabs": "2008arXiv0805.3018F"
    }
  }
}