With the help of split quaternions, rotational motion in Lorentz space can be studied. This rotation corresponds to the rotations on the hyperboloids. The aim of this study is to define and examine hyperbolic rotations in the new geometry space. We describe new quaternions that are called multiplicative hyperbolic split quaternions, in this study. We also defined the geometric hyperbolic scalar product and geometric hyperbolic vector product to be able to study hyperbolical rotations. So, we define geometric hyperbolical rotation matrices. Then, it is also shown visually by giving a few examples through the MAPLE program. Finally, we give geometrical inter- presentations of the results in the multiplicative hyperboloidal split quaternion that come up with these results.

中文翻译：

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乘法双曲分裂四元数并生成几何双曲旋转矩阵


借助分裂四元数，可以研究洛伦兹空间中的旋转运动。该旋转对应于双曲面上的旋转。本研究的目的是定义和检查新几何空间中的双曲旋转。在这项研究中，我们描述了称为乘法双曲分裂四元数的新四元数。我们还定义了几何双曲标量积和几何双曲矢量积，以便能够研究双曲旋转。因此，我们定义几何双曲旋转矩阵。然后，还通过MAPLE程序给出了几个例子来直观地展示出来。最后，我们在乘法双曲面分割四元数中给出了结果的几何表示。