Multiplicity of Scator Roots and the Square Roots in $\\mathbb{S}^{1+2}$

Authors : Manuel Fernandez-guasti

Pages : 29-42

Doi:10.53570/jnt.1188215

View : 15 | Download : 6

Publication Date : 2023-03-31

Article Type : Research

Abstract :This paper presents the roots of elliptic scator numbers in $\\mathbb{S}^{1+n}$, which includes both the fundamental $2\\pi$ symmetry and the $\\pi$-pair symmetry for $n\\geq2$. Here, the scator set $\\mathbb{S}^{1+n}$ is a subset of $\\mathbb{R}^{1+n}$ with the scator product and the multiplicative representation. These roots are expressed in terms of both additive (rectangular) and multiplicative (polar) variables. Additionally, the paper provides a comprehensive description of square roots in $\\mathbb{S}^{1+2}$, which includes a geometrical representation in three-dimensional space that provides a clear visualization of the concept and makes it easier to understand and interpret. Finally, the paper handles whether the aspects should be further investigated.
Keywords : Roots, non-distributive algebras, hypercomplex numbers