Exceptional Projective Geometries and Internal Symmetries

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.

37 pages, 6 figures

Cited by in corpus (4)

• The Geometry of Jordan Matrix Models
• Self-Dual Fields and Quaternion Analyticity
• Symmetries and Mass Predictions of the Supersymmetric Quark Model
• A Jordan GNS Construction for the Holonomy-Flux *-algebra