Involutions of Complexified Quaternions and Split Quaternions

Bekar M., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.23, sa.2, ss.283-299, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s00006-012-0376-y
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.283-299
  • Anahtar Kelimeler: Real quaternions, biquaternions (complexified quaternions), split quaternions, involutions, anti-involutions
  • Ankara Üniversitesi Adresli: Evet

Özet

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.