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

Year 2016, Volume: 28 Issue: 3, 95 - 99, 31.12.2016

https://doi.org/10.7240/mufbed.36025

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.

Flaut, C., & Shpakivskyi V., (2015). An efficient method for solving equations in generalized quaternion and octonion algebras, Advance in Applied Clifford algebra, 25 (2), 337– 350.
Jafari M., On the Properties of Quasi-Quaternions Algebra, (2014). Communications, faculty of science, university of Ankara, Series A1: Mathematics and statistics, 63(1), 1-10.
Jafari M., (2015). A viewpoint on semi-octonion algebra, Journal of Selcuk university natural and applied science, 4(4), 46-53.
Jafari M., (2015). Split Octonion Analysis, Representation Theory and Geometry, Submitted for publication.
Jafari M., Azanchiler H., (2015). On the structure of the octonion matrices, Submitted for publication.
Jafari M., (2015). An Introduction to Quasi-Octonions and Their Representation,
Mortazaasl H., Jafari M., (2013). A study on Semi-quaternions Algebra in Semi-Euclidean 4-Space, Mathematical Sciences and Applications E-Notes, 1(2) 20-27.
Jafari M., (2015). The Fundamental Algebraic Properties of Split Quasi-Octonions, DOI: 10. 13140/RG .2.1.3348.2728
Rosenfeld B. A., Geometry of Lie Groups, Kluwer Academic Publishers, Dordrecht, 1997.

Year 2016, Volume: 28 Issue: 3, 95 - 99, 31.12.2016

https://doi.org/10.7240/mufbed.36025

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.

Flaut, C., & Shpakivskyi V., (2015). An efficient method for solving equations in generalized quaternion and octonion algebras, Advance in Applied Clifford algebra, 25 (2), 337– 350.
Jafari M., On the Properties of Quasi-Quaternions Algebra, (2014). Communications, faculty of science, university of Ankara, Series A1: Mathematics and statistics, 63(1), 1-10.
Jafari M., (2015). A viewpoint on semi-octonion algebra, Journal of Selcuk university natural and applied science, 4(4), 46-53.
Jafari M., (2015). Split Octonion Analysis, Representation Theory and Geometry, Submitted for publication.
Jafari M., Azanchiler H., (2015). On the structure of the octonion matrices, Submitted for publication.
Jafari M., (2015). An Introduction to Quasi-Octonions and Their Representation,
Mortazaasl H., Jafari M., (2013). A study on Semi-quaternions Algebra in Semi-Euclidean 4-Space, Mathematical Sciences and Applications E-Notes, 1(2) 20-27.
Jafari M., (2015). The Fundamental Algebraic Properties of Split Quasi-Octonions, DOI: 10. 13140/RG .2.1.3348.2728
Rosenfeld B. A., Geometry of Lie Groups, Kluwer Academic Publishers, Dordrecht, 1997.

There are 9 citations in total.

APA	Jafarı, M. (2016). On The Para-Octonions; a Non-Associative Normed Algebra. Marmara Fen Bilimleri Dergisi, 28(3), 95-99. https://doi.org/10.7240/mufbed.36025
AMA	Jafarı M. On The Para-Octonions; a Non-Associative Normed Algebra. MFBD. December 2016;28(3):95-99. doi:10.7240/mufbed.36025
Chicago	Jafarı, Mehdi. “On The Para-Octonions; A Non-Associative Normed Algebra”. Marmara Fen Bilimleri Dergisi 28, no. 3 (December 2016): 95-99. https://doi.org/10.7240/mufbed.36025.
EndNote	Jafarı M (December 1, 2016) On The Para-Octonions; a Non-Associative Normed Algebra. Marmara Fen Bilimleri Dergisi 28 3 95–99.
IEEE	M. Jafarı, “On The Para-Octonions; a Non-Associative Normed Algebra”, MFBD, vol. 28, no. 3, pp. 95–99, 2016, doi: 10.7240/mufbed.36025.
ISNAD	Jafarı, Mehdi. “On The Para-Octonions; A Non-Associative Normed Algebra”. Marmara Fen Bilimleri Dergisi 28/3 (December 2016), 95-99. https://doi.org/10.7240/mufbed.36025.
JAMA	Jafarı M. On The Para-Octonions; a Non-Associative Normed Algebra. MFBD. 2016;28:95–99.
MLA	Jafarı, Mehdi. “On The Para-Octonions; A Non-Associative Normed Algebra”. Marmara Fen Bilimleri Dergisi, vol. 28, no. 3, 2016, pp. 95-99, doi:10.7240/mufbed.36025.
Vancouver	Jafarı M. On The Para-Octonions; a Non-Associative Normed Algebra. MFBD. 2016;28(3):95-9.