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          Institute: MPI für Gravitationsphysik     Collection: Quantum Gravity and Unified Theories     Display Documents



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ID: 354851.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Hyperbolic Weyl Groups and the Four Normed Division Algebras
Authors:Feingold, Alex J.; Kleinschmidt, Axel; Nicolai, Hermann
Date of Publication (YYYY-MM-DD):2009
Title of Journal:Journal of Algebra
Volume:322
Start Page:1295
End Page:1339
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
Identifiers:LOCALID:arXiv:0805.3018v1 [math.RT]
DOI:doi:10.1016/j.jalgebra.2009.05.006
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