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

2010/11/11 by Geoffrey Dixon, Dixon, Geoffrey
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Rings and Algebras (math.RA) #hep-th #math.RA

paper · pdf · doi:10.48550/arxiv.1011.2541

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

arxiv created 2010/11/11 · openalex publication_date 2010/11/11 · arxiv updated 2010/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, Λ4, Λ8, Λ16 and Λ24 (Leech), are developed.

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