Year 2016, Volume 4, Issue 2, Pages 99 - 112 2016-08-25

The Real Matrix Representations of Semi-Octonions
THE REAL MATRIX REPRESENTATIONS OF SEMI-OCTONIONS

Mehdi Jafari [1]

402 493

Rosenfeld’s book [6] is a wonderful introduction to the normed division algebras: the real numbers, the complex
numbers, the quaternions, and the octonions. A brief introduction of the semi-octonions is provided in this book. In
[3], we studied some fundamental properties of the semi-octonions, Os, and show that the set of unit semi-octonions
is a subgroup of Os. In this paper, we give a complete investigation to real matrix representations of semi-octonions,
and consider a relation between the powers of these matrices. The De Moivre's formula implies that there are
uncountably many matrices of the unit semi-octonions A satisfying An = I8 for every integer n ≥ 3.
Rosenfeld’in kitabında normlu bölüm cebirleri, reel sayılar, kompleks sayılar, kuaterniyonlar ve oktonyonlara harika bir giriş yapılmıştır [6]. Yarı-oktonyonlara bir ufak giriş bu kitapta bulunabilir. Biz daha önce yarı-oktonyonların (Os) bazı temel özelliklerini inceledik ve gösterdik ki birim yarı-oktonyonların kümesi, O’nin bir alt-kümesidir [3]. Bu makalede, yarıoktonyonların reel matris gösterimini inceleyip aralarındaki bazı ilişkileri verdik. De-Moivre formülü, birim yarı-oktonyonlara karşılık gelen sayılamaz sayıda A matrisinin her n ≥ 3 tam sayısı için An = I8 şeklinde var olduğunu söylemektedir
Alternatiflik, De Moivre’s formülü, Euler’s formülü, Yarı-oktonyon
  • Agrawal O P. Hamilton Operators and Dual number-quaternions in Spatial Kinematics. Mechanism and machine theory 1987; 22(6): 569-575.
  • Jafari M. On the properties of quasi-quaternions algebra, Communications faculty of science University Ankara, Series A, 63(1), 2014.
  • Jafari M. A viewpoint on semi-octonion algebra. Journal of Selçuk university natural and applied Science 2015; 4(4): 46-53.
  • Kansu M E, Tanisli M, Demir S. Electromagnetic energy conservation with complex octonions, Turkish journal of physics 2012; 36: 438–445.
  • Mortazaasl H, Jafari M. A study on semi-quaternions algebra in semi-Euclidean 4-space, Mathematical sciences and applications E-Notes2013; 1(2): 20-27. [6] Rosenfeld B A. Geometry of Lie Groups, Kluwer Academic Publishers, Dordrecht , 1997
Journal Section Articles
Authors

Author: Mehdi Jafari

Dates

Publication Date: August 25, 2016

Bibtex @ { aubtdb262698, journal = {ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences}, issn = {2146-0272}, eissn = {2146-0191}, address = {Eskişehir Teknik Üniversitesi}, year = {2016}, volume = {4}, pages = {99 - 112}, doi = {10.20290/btdb.04545}, title = {The Real Matrix Representations of Semi-Octonions}, key = {cite}, author = {Jafari, Mehdi} }
APA Jafari, M . (2016). The Real Matrix Representations of Semi-Octonions. ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences, 4 (2), 99-112. DOI: 10.20290/btdb.04545
MLA Jafari, M . "The Real Matrix Representations of Semi-Octonions". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences 4 (2016): 99-112 <http://dergipark.org.tr/aubtdb/issue/24860/262698>
Chicago Jafari, M . "The Real Matrix Representations of Semi-Octonions". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences 4 (2016): 99-112
RIS TY - JOUR T1 - The Real Matrix Representations of Semi-Octonions AU - Mehdi Jafari Y1 - 2016 PY - 2016 N1 - doi: 10.20290/btdb.04545 DO - 10.20290/btdb.04545 T2 - ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences JF - Journal JO - JOR SP - 99 EP - 112 VL - 4 IS - 2 SN - 2146-0272-2146-0191 M3 - doi: 10.20290/btdb.04545 UR - https://doi.org/10.20290/btdb.04545 Y2 - 2019 ER -
EndNote %0 ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences The Real Matrix Representations of Semi-Octonions %A Mehdi Jafari %T The Real Matrix Representations of Semi-Octonions %D 2016 %J ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences %P 2146-0272-2146-0191 %V 4 %N 2 %R doi: 10.20290/btdb.04545 %U 10.20290/btdb.04545
ISNAD Jafari, Mehdi . "The Real Matrix Representations of Semi-Octonions". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences 4 / 2 (August 2016): 99-112. https://doi.org/10.20290/btdb.04545
AMA Jafari M . The Real Matrix Representations of Semi-Octonions. AUBTD-B. 2016; 4(2): 99-112.
Vancouver Jafari M . The Real Matrix Representations of Semi-Octonions. ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences. 2016; 4(2): 112-99.