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Hyperbolic Weyl groups and the four normed division algebras

Authors
  • Feingold, Alex J.
  • Kleinschmidt, Axel
  • Nicolai, Hermann
Type
Published Article
Publication Date
Jul 14, 2017
Submission Date
May 20, 2008
Identifiers
DOI: 10.1016/j.jalgebra.2009.05.006
Source
arXiv
License
Yellow
External links

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.

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