English

The complex Lorentzian Leech lattice and the bimonster

Group Theory 2007-05-23 v2 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0508228,
  title  = {The complex Lorentzian Leech lattice and the bimonster},
  author = {Tathagata Basak},
  journal= {arXiv preprint arXiv:math/0508228},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T17:23:01.686Z