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.
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Articles |
Yazarlar | |
Yayımlanma Tarihi | 31 Ekim 2023 |
Gönderilme Tarihi | 7 Ekim 2022 |
Kabul Tarihi | 23 Ekim 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 11 Sayı: 2 |