INVOLUTIONS IN SEMI-QUATERNIONS


Bekar M. , Yayli Y.

JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, vol.41, pp.1-16, 2016 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41
  • Publication Date: 2016
  • Doi Number: 10.7546/jgsp-41-2016-1-16
  • Title of Journal : JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS
  • Page Numbers: pp.1-16

Abstract

Involutions are self-inverse and homomorphic linear mappings. Rotations, reflections and rigid-body (screw) motions in three-dimensional Euclidean space R-3 can be represented by involution mappings obtained by quaternions. For example, a reflection of a vector in a plane can be represented by an involution mapping obtained by real-quaternions, while a reflection of a line about a line can be represented by an involution mapping obtained by dual-quaternions. In this paper, we will consider two involution mappings obtained by semi-quternions, and a geometric interpretation of each as a planar-motion in R-3.