The complex Lorentzian Leech lattice and the bimonster

Details The complex Lorentzian Leech lattice and the bimonster The complex Lorentzian Leech lattice and the bimonster

2005-08-13

arxiv.org/abs/math/0508228v2

Mathematics

Group Theory

24 pages, 3 figures, revised and proof corrected. Some small results added. to appear in the Journal of Algebra

Scientific paper

We find 26 reflections in the automorphism group of the the Lorentzian Leech lattice L over Z[exp(2*pi*i/3)] that form the Coxeter diagram seen in the presentation of the bimonster. We prove that these 26 reflections generate the automorphism group of L. We find evidence that these reflections behave like the simple roots and the vector fixed by the diagram automorphisms behaves like the Weyl vector for the refletion group.

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