Involutions of Complexified Quaternions and Split Quaternions


Bekar M. , Yayli Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.23, no.2, pp.283-299, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.1007/s00006-012-0376-y
  • Title of Journal : ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Page Numbers: pp.283-299

Abstract

An involution or anti-involution is a self-inverse linear mapping. Involutions and anti-involutions of real quaternions were studied by Ell and Sangwine [15]. In this paper we present involutions and antiinvolutions of biquaternions (complexified quaternions) and split quaternions. In addition, while only quaternion conjugate can be defined for a real quaternion and split quaternion, also complex conjugate can be defined for a biquaternion. Therefore, complex conjugate of a biquaternion is used in some transformations beside quaternion conjugate in order to check whether involution or anti-involution axioms are being satisfied or not by these transformations. Finally, geometric interpretations of real quaternion, biquaternion and split quaternion involutions and anti-involutions are given.