Integral Octonions, Octonion XY-Product, and the Leech Lattice

Abstract

The integral octonions arise from the octonion XY-product. A parallel is shown to exist with the quaternion Z-product. Connections to the laminated lattices, ${\Lambda }_4$, ${\Lambda }_8$, ${\Lambda }_{16}$ and ${\Lambda }_{24}$ (Leech), are developed.

arXiv commentMuch of this work was presented at an AMS conference at Notre Dame in November 2010

References in corpus (3)

• Octonion X-product orbits
• OCTONION XY-PRODUCT
• OCTONIONS: INVARIANT LEECH LATTICE EXPOSED