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

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

Mehdi Jafarı

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

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

References

  • 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.

Para-Ktonyonlar Üzerine; Bir İlişkisel Olmayan Normlu Cebir

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

Mehdi Jafarı

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

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

References

  • 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.

Details

Subjects Engineering
Journal Section Research Articles
Authors

Mehdi Jafarı

Publication Date December 31, 2016
Acceptance Date October 6, 2016
Published in Issue Year 2016 Volume: 28 Issue: 3

Cite

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. MAJPAS. 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”, MAJPAS, 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. MAJPAS. 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. MAJPAS. 2016;28(3):95-9.

Marmara Journal of Pure and Applied Sciences

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