INVOLUTIONS IN SEMI-QUATERNIONS
JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, vol.41, pp.1-16, 2016 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 41
- Publication Date: 2016
- Doi Number: 10.7546/jgsp-41-2016-1-16
- Journal Name: JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.1-16
- Keywords: Dual-quaternions, involutions, planar-motion, semi-quaternions
- Open Archive Collection: AVESIS Open Access Collection
- Ankara University Affiliated: Yes
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.