Involutions in Dual Split-Quaternions


Bekar M., Yayli Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.26, no.2, pp.553-571, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s00006-015-0624-z
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.553-571
  • Keywords: Real-quaternions, dual split-quaternions, involutions, anti-involutions, rigid-body (screw) motions, TRANSPOSITION ANTI-INVOLUTION, SCREW MOTION, CLIFFORD
  • Gazi University Affiliated: No

Abstract

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 .