Clifford Product and Lorentzian Plane Displacements In 3-Dimensional Lorentzian Space

In this paper, by defining Clifford algebra product in 3-dimensional Lorentz space, L ³, it is shown that even Clifford algebra of L ³ corresponds to split quaternion algebra. Then, by using Lorentzian matrix multiplication, pole point of planar displacement in Lorentz plane L ² is obtained. In addition, by defining degenerate Lorentz scalar product for L ³ and by using the components of pole points of Lorentz plane displacement in particular split hypercomplex numbers, it is shown that the Lorentzian planar displacements can be represented as a special split quaternion which we call it Lorentzian planar split quaternion.