OCTONIONS: INVARIANT REPRESENTATION OF THE LEECH LATTICE

Abstract

The Leech lattice, ${\Lambda }_{24}$, is represented on the space of octonionic 3-vectors. It is built from two octonionic representations of $E_8$, and is reached via ${\Lambda }_{16}$. It is invariant under the octonion index cycling and doubling maps.

7 pages, latex, no figures