Involutions in semi-quaternions. (English) Zbl 1404.51019

Bekar, Murat; Yayli, Yusuf

J. Geom. Symmetry Phys. 41, 1-16 (2016).

Summary: Involutions are self-inverse and homomorphic linear mappings. Rotations, reflections and rigid-body (screw) motions in three-dimensional Euclidean space \(\mathbb R^3\) 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 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 \(\mathbb R^3\).

MSC:

51N20	Euclidean analytic geometry
11R52	Quaternion and other division algebras: arithmetic, zeta functions
53A30	Conformal differential geometry (MSC2010)

Keywords:

dual-quaternions; involutions; planar-motion; semi-quaternions