Exceptional Projective Geometries and Internal Symmetries
Exceptional Projective Geometries and Internal Symmetries
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发表时间：
2003-02
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通讯作者：
S. Catto
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作者：
S. Catto
一种新的气动装置与O(7)数值张量一起出现，它表现出对偶性，并反映了7维空间的自然7=(4+3)分裂。然后，德沙格和帕普斯的定理被证明是通过一个几何联系在一起的，该几何利用了表现这种对偶性的八元数。利用Jordan代数和例外射影几何构造了例外Hilbert空间。简要讨论了Moufang平面和非笛卡尔几何。
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.