On The Para-Octonions; a Non-Associative Normed Algebra

Abstract

In this paper, para-octonions and their algebraic properties are provided by using the Cayley-Dickson multiplication rule between the octonionic

basis elements. The trigonometric form of a para-octonion is similar to the trigonometric form of dual number and quasi-quaternion.

We study the De-Moivre’s theorem for para-octonions, extending results obtained for real octonions and defining generalize Euler’s

formula for para-octonions.

Keywords

• Alternativity,Cayley-Dickson construction,De-Moivre’s formula,Para-octonion

Para-Ktonyonlar Üzerine; Bir İlişkisel Olmayan Normlu Cebir

Abstract

Bu çalışmada, octonyonik baz elemanları arasında Cayley-Dickson çarpım kuralı kullanılarak para-octonyonlar ve cebirsel özellikleri verilmiştir.

Bir para-octonyonun trigonometrik formu bir dual-sayının ve bir quasi-kuaterniyonun trigonometrik formuna benzerdir. Para-octonyonlar

içn De-Moivre’nin teoremi ele alınarak reel-octonyonlar için elde edilen sonuçlar genelleştirilmiştir. Ayrıca, para-octonyonlar

için genel Euler formülleri tanımlanmıştır.

Keywords

• Alternatiflik,Cayley-Dickson yapı,De-Moivre formu,para-oktoniyon

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