Involutions in Dual Split-Quaternions

Bekar M., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.26, sa.2, ss.553-571, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00006-015-0624-z
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.553-571
  • Anahtar Kelimeler: Real-quaternions, dual split-quaternions, involutions, anti-involutions, rigid-body (screw) motions, TRANSPOSITION ANTI-INVOLUTION, SCREW MOTION, CLIFFORD
  • Ankara Üniversitesi Adresli: Evet

Özet

Involutions and anti-involutions are self-inverse linear mappings. In three-dimensional Euclidean space , a reflection of a vector in a plane can be represented by an involution or anti-involution mapping obtained by real-quaternions. A reflection of a line about a line in can also be represented by an involution or anti-involution mapping obtained by dual real-quaternions. In this paper, we will represent involution and anti-involution mappings obtaind by dual split-quaternions and a geometric interpretation of each as rigid-body (screw) motion in three-dimensional Lorentzian space .