Abstract The Lie sphere geometry is a natural extension of the Mobius geometry, where the latter is very important in string theory and the AdS/CFT correspondence. The extension to Lie sphere geometry is applied in the following to a sequence of Mobius geometries, which has been investigated recently in a bicomplex matrix representation. When higher dimensional space-time geometries are invoked by inverse projections starting from an originating point geometry, the Lie sphere scheme provides a more natural structure of the involved Clifford algebras compared to the previous representation. The spin structures resulting from the generated Clifford algebras can potentially be used for the geometrization of internal particle symmetries. A simple model, which includes the electromagnetic spin, the weak isospin, and the hadronic isospin, is suggested for further verification.

中文翻译：

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核散射过程中的李球几何

摘要 李球几何是莫比乌斯几何的自然延伸，后者在弦论和 AdS/CFT 对应关系中非常重要。Lie 球几何的扩展在下文中应用于一系列 Mobius 几何，最近在双复矩阵表示中对其进行了研究。当更高维的时空几何通过从原始点几何开始的逆投影调用时，与之前的表示相比，李球方案提供了所涉及的 Clifford 代数的更自然的结构。由生成的 Clifford 代数产生的自旋结构可以潜在地用于内部粒子对称性的几何化。一个简单的模型，包括电磁自旋、弱同位旋和强子同位旋，