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arXiv · hep-th/0302079

Exceptional Projective Geometries and Internal Symmetries

Sultan Catto
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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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Sultan Catto. 2003-02-11. Exceptional Projective Geometries and Internal Symmetries. https://arxiv.org/abs/hep-th/0302079

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