Algebraic structure and basics of analysis of n-dimensional quaternionic space

Altun D., YÜCE S.

Heliyon, vol.7, no.6, 2021 (ESCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1016/j.heliyon.2021.e07375
  • Journal Name: Heliyon
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, CAB Abstracts, Food Science & Technology Abstracts, Veterinary Science Database, Directory of Open Access Journals
  • Keywords: Symplectic geometry, n-Dimensional quaternionic space, Componentwise multiplication
  • Istanbul Gelisim University Affiliated: No

Abstract

In this study, we focused on n-dimensional quaternionic space Hn. To create the module structure, first part is devoted to define a metric depending on the product order relation of Rn. The set of Hn has been rewritten with a different representation of n-vectors. Using this notation, formulations corresponding to the basic operations in Hn are obtained. By adhering these representations, module structure of Hn over the set of real ordered n-tuples is given. Afterwards, we gave limit, continuity and the derivative basics of quaternion valued functions of a real variable.