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Quaternions Algebra and Its Applications: An Overview

Received: 3 October 2016     Accepted: 9 December 2016     Published: 10 December 2016
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Abstract

The real quaternions algebra was invented by W.R. Hamilton as an extension to the complex numbers. In this paper, we study various kinds of quaternions and investigate some of basic algebraic properties and geometric applications of them.

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI 10.11648/j.ijtam.20160202.18
Page(s) 79-85
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Generalized Quaternion, Rotation, Split Quaternion, Quasi-Quaternion, Homothetic Motion

References
[1] Jafari M., Yayli Y., Generalized quaternions and their algebraic properties, Communications, faculty of science, university of Ankara, Series A1: Mathematics and statistics, Vol. 64(1), 15-27, 2015.
[2] Jafari M., Yayli Y., Homothetic motions at E4αβ, International journal contemporary of mathematics sciences, Vol. 5 (47) 2319-2326, 2010.
[3] Jafari M., Matrix algebras in E4αβ and their applications, E-journal of new world sciences academy, NWSA-physical science, Vol. 10(1) 2015.
[4] Jafari M., Yayli Y., Four dimensions via generalized Hamilton operators, Kuwait journal of science, Vol. 40(1) 67-79, 2013.
[5] Jafari M., Yayli Y., Generalized quaternions and Rotation in 3-space, TWMS Journal of pure and applied mathematics, Vol. 6(2) 224-232, 2015.
[6] Jafari M., Mortazaasl H., Yayli Y., De-Moivre’s formula for matrices of quaternions, JP journal of algebra, number theory and application, Vol. 21(1) 57-67, 2011.
[7] Jafari M., Yayli Y., Matrix theory over the split quaternions, International journal of geometry, Vol. 3 (2), 57-69, 2014.
[8] Jafari M., A Survey on Matrix Algebra in Semi Euclidean Space, DOI: 10.13140/RG.2.1.4613.8087
[9] Jafari M., Matrix formulation of real quaternions, Erzincan university journal of science & technology, Vol. 8(1), 2015, 27-37.
[10] Jafari M., Split Semi-quaternions algebra in Semi-Euclidean 4-space, Cumhuriyet Science Journal, Vol. 36 (1), 2015, 70-77.
[11] Jafari M, Molaei H., Some properties of matrix algebra of semi-quaternios, Cumhuriyet Science Journal, Vol. 36 (5), 2015, 70-77.
[12] Jafari M., Yayli Y., One-parameter Homothetic motions in the Minkowski 3-space, TWMS journal of applied and engineering mathematics, Vol. 6 (1) 2016, 84-91.
[13] Jafari M., Kinematics on the generalized 3-space, NWSA: Physical Sciences, E-Journal of New World Sciences Academy, Vol. 10 (4), 2015, 55-63.
[14] Jafari M., Kinematics mapping in semi-Euclidean 4-sapce, Duzce university journal of science and Technology, 3(2015) 173-179.
[15] Jafari M., Advances in the Semi-quaternionic matrices, https://www.researchgate.net/publication/292986883
[16] Jafari M., Some results on the matrices of Split Semi-quaternions, https://www.researchgate.net/publication /292986884
[17] Jafari M., Homothetic motions in the generalized 3-space, Anadolu university journal of science and technology B, Theoretical science, Vol. 4(1), 2016, 43-51.
[18] Jafari M., Homothetic motions in Euclidean 3-space, Kuwait Journal of Science, Vol. 41(1), 65-73, 2014.
[19] Jafari M., On the properties of quasi-quaternions algebra, Communications, faculty of science, university of Ankara, Series A1: Mathematics and statistics, Vol. 63(1), 1-10, 2014.
[20] Kula L., Yayli Y., Split quaternions and rotations in semi-Euclidean space , Journal of Korean Math. Soc. 44(6) 1313-1327, 2007.
[21] Kula L., Yayli Y., Homothetic Motions in semi-Euclidean space. Proceedings of the Royal Irish Academy, Vol. 105, Section A, 2005.
[22] Mortazaasl H., Jafrai M., A study on semi-quaternions algebras in semi-Euclidean 4-space, Mathematical sciences and applications E-notes, Vol. 1(2), 2013, 20-27.
[23] Pottman H., Wallner J., Computational line geometry. Springer-Verlag Berlin Heidelberg New York, 2000.
[24] Quaternions, https://en.wikipedia.org/wiki/Quaternion
[25] Rosenfeld B. A., Geometry of Lie groups, Kluwer academic publishers, Dordrecht, 1997.
[26] Split-quaternion, https://en.wikipedia.org/wiki/ Splitquaternion
[27] Savin D., Flaut C., Ciobanu C., Some properties of the symbol algebras, Carpathian journal Mathematics, arXiv: 0906.2715v1, 2009.
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    Mehdi Jafari. (2016). Quaternions Algebra and Its Applications: An Overview. International Journal of Theoretical and Applied Mathematics, 2(2), 79-85. https://doi.org/10.11648/j.ijtam.20160202.18

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    ACS Style

    Mehdi Jafari. Quaternions Algebra and Its Applications: An Overview. Int. J. Theor. Appl. Math. 2016, 2(2), 79-85. doi: 10.11648/j.ijtam.20160202.18

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    AMA Style

    Mehdi Jafari. Quaternions Algebra and Its Applications: An Overview. Int J Theor Appl Math. 2016;2(2):79-85. doi: 10.11648/j.ijtam.20160202.18

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  • @article{10.11648/j.ijtam.20160202.18,
      author = {Mehdi Jafari},
      title = {Quaternions Algebra and Its Applications: An Overview},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {2},
      number = {2},
      pages = {79-85},
      doi = {10.11648/j.ijtam.20160202.18},
      url = {https://doi.org/10.11648/j.ijtam.20160202.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.18},
      abstract = {The real quaternions algebra was invented by W.R. Hamilton as an extension to the complex numbers. In this paper, we study various kinds of quaternions and investigate some of basic algebraic properties and geometric applications of them.},
     year = {2016}
    }
    

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Author Information
  • Department of Mathematics, Technical and Vocational University, Urmia, Iran

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