将3d四元数维度拆分为2d-sells和“世界屏幕技术”
Splitting of 3d quaternion dimensions into 2d-sells and a "world screen technology"
摘要：
一组局部描述任意二维（2D）表面的度量性质的基本向量用于构造具有幂零和幂等性质的基本代数对象。它表明，所有可能的线性组合的对象相乘时表现为一组超复数（特别是四元数）单位，从而暴露的内部结构的三维空间尺寸指向的矢量单位。几何表示的基本表面（2D销售）结构的尺寸进行了详细研究。在被视为3D空间中的帧的矢量四元数三元组和基本2D销售之间建立的数学联系提示提出具有1/2空间维度但充分反映3D帧的集合的运动学性质的“世界屏幕”的想法。
英文摘要：
A set of basic vectors locally describing metric properties of an arbitrary 2-dimensional (2D) surface is used for construction of fundamental algebraic objects having nilpotent and idempotent properties. It is shown that all possible linear combinations of the objects when multiplied behave as a set of hypercomples (in particular, quaternion) units; thus interior structure of the 3D space dimensions pointed by the vector units is exposed. Geometric representations of elementary surfaces (2D-sells) structuring the dimensions are studied in detail. Established mathematical link between a vector quaternion triad treated as a frame in 3D space and elementary 2D-sells prompts to raise an idea of "world screen" having 1/2 of a space dimension but adequately reflecting kinematical properties of an ensemble of 3D frames.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
