One Parameter Commutative Octonions

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Konuralp Journal of Mathematics
Volume:11 Issue:2
One Parameter Commutative Octonions

One Parameter Commutative Octonions

Authors : Göksal Bilgici

Pages : 169-175

View : 42 | Download : 88

Publication Date : 2023-10-31

Article Type : Research Paper

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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