Abstract In this paper, we introduce and define hyper-dual split vectors by using hyper-dual numbers. We define three subsets; two of them are subsets of Lorentzian unit hyper-dual sphere and the other is a subset of hyperbolic unit hyper-dual sphere. We show that to each element of these subsets corresponds two intersecting perpendicular lines in Minkowski space. We also introduce and define hyper-dual split quaternions with their basic algebraic properties. We give the geometric interpretation of hyper-dual split quaternions, and we define three new operators in Minkowski space. We show that these operators turn each two intersecting perpendicular lines again to two intersecting perpendicular lines in Minkowski space. Examples are also provided to illustrate our theorems and results.

中文翻译：

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超双分裂四元数和刚体运动

摘要 在本文中，我们使用超对偶数来介绍和定义超对偶分裂向量。我们定义了三个子集；其中两个是洛伦兹单位超对偶球的子集，另一个是双曲单位超对偶球的子集。我们证明这些子集的每个元素对应于闵可夫斯基空间中的两条相交垂直线。我们还介绍并定义了具有基本代数性质的超双分裂四元数。我们给出了超双分裂四元数的几何解释，并在闵可夫斯基空间中定义了三个新算子。我们证明这些算子将每两条相交的垂直线再次转换为闵可夫斯基空间中的两条相交的垂直线。还提供了示例来说明我们的定理和结果。