Generalized Split Quaternions and Their Applications on Non-Parabolic Conical Rotations

Duru M., ÇOLAKOĞLU H. B.

Symmetry, vol.15, no.9, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 9
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15091805
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Lorentzian inner product, Lorentzian rotation matrix, Lorentzian symmetry, Lorentzian vector product, split quaternion
  • Akdeniz University Affiliated: Yes

Abstract

In this study, we first generalize the Lorentzian inner and vector products, and then we define the generalized split quaternions by means of the generalized Lorentzian inner and vector products. Next, on any hyperboloid of one or two sheets, which is a generalized Lorentzian sphere, non-parabolic conical rotations with nonnull axes are expressed using the generalized split quaternions with supporting numerical examples.