On geometric interpretations of split quaternions


Öztürk İ., ÖZDEMİR M.

Mathematical Methods in the Applied Sciences, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1002/mma.8518
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Lorentzian geometry, non-euclidean rotations, quaternions, split quaternions (coquaternions)
  • Akdeniz University Affiliated: Yes

Abstract

© 2022 John Wiley & Sons, Ltd.Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).