Exceptional Projective Geometries and Internal Symmetries

2003/02/11 by Sultan Catto, Catto, Sultan · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Mathematics and Applications #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0302079

37 pages, 6 figures

arxiv created 2003/02/11 · arxiv updated 2009/11/30

Abstract

A new mneumonic device is shown to emerge in connection with O(7) numerical tensors exhibiting duality and reflecting the natural 7=(4+3) splitting of 7-dimensional space. Then Desargues' and Pappus' theorems are shown to be connected through a geometry that makes use of octonionic numbers exhibiting this duality. Construction of exceptional Hilbert space based on Jordan algebras and exceptional projective geometries is illustrated. A brief discussion of the Moufang plane and non-Desarguesian geometries is presented.

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