Exceptional Projective Geometries and Internal Symmetries
High Energy Physics - Theory
2007-05-23 v1
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.
Cite
@article{arxiv.hep-th/0302079,
title = {Exceptional Projective Geometries and Internal Symmetries},
author = {Sultan Catto},
journal= {arXiv preprint arXiv:hep-th/0302079},
year = {2007}
}
Comments
37 pages, 6 figures