Open Access
2016 Involutions in Semi-Quaternions
Murat Bekar, Yusuf Yayli
J. Geom. Symmetry Phys. 41: 1-16 (2016). DOI: 10.7546/jgsp-41-2016-1-16


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 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 $\mathbb{R}^3$.


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Murat Bekar. Yusuf Yayli. "Involutions in Semi-Quaternions." J. Geom. Symmetry Phys. 41 1 - 16, 2016.


Published: 2016
First available in Project Euclid: 31 May 2017

zbMATH: 06683084
MathSciNet: MR3585163
Digital Object Identifier: 10.7546/jgsp-41-2016-1-16

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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