One Parameter Commutative Octonions

Year 2023, Volume: 11 Issue: 2, 169 - 175, 31.10.2023

Göksal Bilgici

Abstract

Hyperbolic numbers had been developed in the 19th century. Octonions forms a noncommutative and nonassociative normed division algebra over reals. Octonions have many applications in fields of physics such as quantum logic and string theory. Cayley-Dickson process is applied to quaternions in order to construct octonions and in a sense, we follow a similar process. The aim of this study is to introduce the concept of commutative octonions. We construct this algebra by using some matrix methods. After construction, we give a number of properties of commutative octonions such as fundamental matrices and principal conjugates. We also obtain representation of a commutative octonion as decomposed form, holomorphic and analytic functions of commutative octonions.

Keywords

Commutative octonions, Segre, holomorphic functions

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