Clifford product and lorentzian plane displacements in 3-dimensional Lorentzian space

Gündoǧan H., ÖZKALDI KARAKUŞ S.

Advances in Applied Clifford Algebras, vol.19, no.1, pp.43-50, 2009 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1007/s00006-008-0124-5
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.43-50
  • Keywords: Clifford algebra, Lorentzian space, Split quaternion
  • Bilecik Şeyh Edebali University Affiliated: No

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. © 2008 Birkhauser.