×

Involutions in semi-quaternions. (English) Zbl 1404.51019

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)
PDF BibTeX XML Cite
Full Text: DOI Link