Hyperbolic Weyl groups and the four normed division algebras

Details Hyperbolic Weyl groups and the four normed division algebras Hyperbolic Weyl groups and the four normed division algebras

2008-05-20

arxiv.org/abs/0805.3018v1

J.Algebra 322:1295-1339,2009

Mathematics

Representation Theory

56 pages, 21 figures

Scientific paper

10.1016/j.jalgebra.2009.05.006

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.

Affiliated with

Also associated with

No associations

Rating

Hyperbolic Weyl groups and the four normed division algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperbolic Weyl groups and the four normed division algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic Weyl groups and the four normed division algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-299976