2014/05/22 by Cristina Flaut, Flaut, Cristina, Vitalii Shpakivskyi +1
Engineering · Mathematics · #Algebraic and Geometric Analysis #Control and Dynamics of Mobile Robots #Dynamics and Control of Mechanical Systems #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1405.5652
openalex publication_date 2014/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quaternions often appear in wide areas of applied science and engineering\nsuch as wireless communications systems, mechanics, etc. It is known that are\ntwo types of non-isomorphic generalized quaternion algebras, namely: the\nalgebra of quaternions and the algebra of coquaternions. In this paper, we\npresent the formulae to pass from a basis in the generalized quaternion\nalgebras to a basis in the division quaternions algebra or to a basis in the\ncoquaternions algebra and vice versa. The same result was obtained for the\ngeneralized octonion algebra. Moreover, we emphasize the applications of these\nresults to the algebraic equations and De Moivre s formula in generalized\nquaternion algebras and in generalized octonion division algebras.\n