{
"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"
}
}
}