Abstract.
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.
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Gündoğan, H., Özkaldi, S. Clifford Product and Lorentzian Plane Displacements In 3-Dimensional Lorentzian Space. AACA 19, 43–50 (2009). https://doi.org/10.1007/s00006-008-0124-5
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DOI: https://doi.org/10.1007/s00006-008-0124-5