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

Gündoǧan H., ÖZKALDI KARAKUŞ S.

Advances in Applied Clifford Algebras, cilt.19, sa.1, ss.43-50, 2009 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 1
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00006-008-0124-5
  • Dergi Adı: Advances in Applied Clifford Algebras
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.43-50
  • Anahtar Kelimeler: Clifford algebra, Lorentzian space, Split quaternion
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Hayır

Özet

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.