Geometric 3-space and multiplicative quaternions

Aslan S., BEKAR M., YAYLI Y.

International Journal of Geometric Methods in Modern Physics, vol.20, no.9, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 9
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219887823501517
  • Journal Name: International Journal of Geometric Methods in Modern Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Geometric 3-space, multiplicative quaternions, geometric angle, geometric circle, geometric sphere, geometric rotation
  • Gazi University Affiliated: Yes

Abstract

In this paper, we introduce a new vector space, the three-dimensional geometric real vector space ℝ3(G), and a new number system, multiplicative quaternions ℍ(G). We give some basic algebraic properties of these concepts. We define spatial rotation in ℝ3(G) by using multiplicative quaternions. Finally, we give an example to illustrate our results.