2018/07/12 by Lahcen Lamgouni, Lamgouni, Lahcen
Mathematics · Physics and Astronomy · #51A25 #51N30 #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Relativity and Gravitational Theory #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1807.04389
openalex publication_date 2018/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we introduce and study the concept of spherical-vectors, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational properties of these distinct vectors, followed by a demonstration, through the transfer of structure, that spherical-vectors constitute a non-abelian additive group, isomorphic to the group of unit quaternions. This identification facilitates the presentation of a novel polar form of quaternions, highlighting its algebraic properties, as well as the algebraic properties of the exponential writing. Furthermore, it enables the depiction of unit quaternions on the unit sphere of ℝ3, allowing for a geometric interpretation of their multiplication.