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

Author： Gündoğan Halit  

Publisher： Springer Publishing Company

ISSN： 0188-7009

Source： Advances in Applied Clifford Algebras, Vol.19, Iss.1, 2009-02, pp. : 43-50

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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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