Involutions in split semi‐quaternions

摘要

> A map is an involution (resp, anti‐involution) if it is a self‐inverse homomorphism (resp, antihomomorphism) of a field algebra. The main purpose of this paper is to show how split semi‐quaternions can be used to express half‐turn planar rotations in 3‐dimensional Euclidean space R 3 and how they can be used to express hyperbolic‐isoclinic rotations in 4‐dimensional semi‐Euclidean space R 3 , 1 . We present an involution and an anti‐involution map using split semi‐quaternions and give their geometric interpretations as half‐turn planar rotations in R 3