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GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES

Year 2015, Volume: 64 Issue: 1, 15 - 27, 01.02.2015
https://doi.org/10.1501/Commua1_0000000724

References

  • Adler S. L., Quaternionic quantum mechanics and quantum …elds, Oxford university press inc., New York, 1995.
  • Agrawal O. P., Hamilton operators and dual-number-quaternions in spatial kinematics, Mech. Mach. theory. Vol. 22, no.6(1987)569-575.
  • Cackle J., On system of algebra involving more than one imaginary, Philosophical magazine, (3) (1849) 434-445.
  • Cho E., De-Moivre Formula for Quaternions, Appl. Math. Lett., Vol. 11, no.6(1998)33-35.
  • Girard P. R., Quaternions, Cliğ ord algebras relativistic physics. Birkhäuser Verlag AG, CH-4010 Basel, Switzerland Part of Springer Science+Business Media, 2007.
  • Inoguchi J., Timelike surfaces of constant mean curvature in Minkowski 3-space, Tokyo J. Math.Vol. 21, no.1(1998)140-152.
  • Hamilton W. Rowan, Elements of quaternions, 2 Vols(1899-1901); reprinted Chelsea, New York, 1969.
  • Jafari M.,On the properties of quasi-quaternion algebra commun.Fac.Sci.Ank.Series A1 vol- ume 63 no 1 (2014) 1303-5991.
  • Jafari M., Yayli Y., Hamilton Operators and Generalized Quaternions, 8thCongress of geometry, Antalya, Turkey. Jafari M., Yayli Y., Homothetic Motions at E4:Int. J. Contemp. Math. Sciences, Vol. 5, no. 47(2010)2319 - 2326.
  • Jafari M., Yayli Y., Hamilton operators and dual generalized quaternions. Work in progress. Jafari M., Yayli Y., Dual Generalized Quaternions in Spatial Kinematics. 41stAnnual Iranian Math. Conference, Urmia, Iran (2010).
  • Kula L. and Yayli Y., Split Quaternions and Rotations in Semi-Euclidean Space E42;J. Korean Math. Soc. 44, no. 6(2007)1313-1327.
  • Karger A., Novak J., Space kinematics and Lie groups, Gordon and science publishers, Kuipers J. B., Quaternions and Rotation Sequences. Published by princenton university press, New Jersey,1999.
  • Mamagani A. B., Jafari M.,On properties of generalized quaternion algebra Journal of novel applied science (2013) 683-689.
  • Mortazaasl H., Jafari M., A study of semi-quaternions algebra in semi-euclidean 4-space. Mathematical Science and applications E-notes Vol. 2(1) (2013) 20-27.
  • ONeill B., Semi-Riemannian geometry, Pure and application mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, pablishers], New York, 1983.
  • Ozdemir M., The roots of a split quaternion, Applied Math. Lett.22(2009) 258-263.
  • Pottman H.,Wallner J., Computational line geometry. Springer-Verlag Berlin Heidelberg New York, 2000.
  • Rosenfeld B., Geometry of Lie groups, Kluwer Academic Publishers, Netherlands,1997.
  • Savin D., Flaut C., Ciobanu C., Some properties of the symbol algebras. Carpathian J. Math.(2009)arXiv:0906.2715v1.
  • Unger T., Markin N., Quadratic forms and space-Time block codes from generalized quater- nion and biquaternion algebras. (2008)arXiv:0807.0199v1.
  • Ward J.P., Quaternions and cayley algebra and applications, Kluwer Academic Publishers, Dordrecht, 1996.
Year 2015, Volume: 64 Issue: 1, 15 - 27, 01.02.2015
https://doi.org/10.1501/Commua1_0000000724

References

  • Adler S. L., Quaternionic quantum mechanics and quantum …elds, Oxford university press inc., New York, 1995.
  • Agrawal O. P., Hamilton operators and dual-number-quaternions in spatial kinematics, Mech. Mach. theory. Vol. 22, no.6(1987)569-575.
  • Cackle J., On system of algebra involving more than one imaginary, Philosophical magazine, (3) (1849) 434-445.
  • Cho E., De-Moivre Formula for Quaternions, Appl. Math. Lett., Vol. 11, no.6(1998)33-35.
  • Girard P. R., Quaternions, Cliğ ord algebras relativistic physics. Birkhäuser Verlag AG, CH-4010 Basel, Switzerland Part of Springer Science+Business Media, 2007.
  • Inoguchi J., Timelike surfaces of constant mean curvature in Minkowski 3-space, Tokyo J. Math.Vol. 21, no.1(1998)140-152.
  • Hamilton W. Rowan, Elements of quaternions, 2 Vols(1899-1901); reprinted Chelsea, New York, 1969.
  • Jafari M.,On the properties of quasi-quaternion algebra commun.Fac.Sci.Ank.Series A1 vol- ume 63 no 1 (2014) 1303-5991.
  • Jafari M., Yayli Y., Hamilton Operators and Generalized Quaternions, 8thCongress of geometry, Antalya, Turkey. Jafari M., Yayli Y., Homothetic Motions at E4:Int. J. Contemp. Math. Sciences, Vol. 5, no. 47(2010)2319 - 2326.
  • Jafari M., Yayli Y., Hamilton operators and dual generalized quaternions. Work in progress. Jafari M., Yayli Y., Dual Generalized Quaternions in Spatial Kinematics. 41stAnnual Iranian Math. Conference, Urmia, Iran (2010).
  • Kula L. and Yayli Y., Split Quaternions and Rotations in Semi-Euclidean Space E42;J. Korean Math. Soc. 44, no. 6(2007)1313-1327.
  • Karger A., Novak J., Space kinematics and Lie groups, Gordon and science publishers, Kuipers J. B., Quaternions and Rotation Sequences. Published by princenton university press, New Jersey,1999.
  • Mamagani A. B., Jafari M.,On properties of generalized quaternion algebra Journal of novel applied science (2013) 683-689.
  • Mortazaasl H., Jafari M., A study of semi-quaternions algebra in semi-euclidean 4-space. Mathematical Science and applications E-notes Vol. 2(1) (2013) 20-27.
  • ONeill B., Semi-Riemannian geometry, Pure and application mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, pablishers], New York, 1983.
  • Ozdemir M., The roots of a split quaternion, Applied Math. Lett.22(2009) 258-263.
  • Pottman H.,Wallner J., Computational line geometry. Springer-Verlag Berlin Heidelberg New York, 2000.
  • Rosenfeld B., Geometry of Lie groups, Kluwer Academic Publishers, Netherlands,1997.
  • Savin D., Flaut C., Ciobanu C., Some properties of the symbol algebras. Carpathian J. Math.(2009)arXiv:0906.2715v1.
  • Unger T., Markin N., Quadratic forms and space-Time block codes from generalized quater- nion and biquaternion algebras. (2008)arXiv:0807.0199v1.
  • Ward J.P., Quaternions and cayley algebra and applications, Kluwer Academic Publishers, Dordrecht, 1996.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Mehdi Jafarı This is me

Yusuf Yaylı This is me

Publication Date February 1, 2015
Published in Issue Year 2015 Volume: 64 Issue: 1

Cite

APA Jafarı, M., & Yaylı, Y. (2015). GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(1), 15-27. https://doi.org/10.1501/Commua1_0000000724
AMA Jafarı M, Yaylı Y. GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2015;64(1):15-27. doi:10.1501/Commua1_0000000724
Chicago Jafarı, Mehdi, and Yusuf Yaylı. “GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64, no. 1 (February 2015): 15-27. https://doi.org/10.1501/Commua1_0000000724.
EndNote Jafarı M, Yaylı Y (February 1, 2015) GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64 1 15–27.
IEEE M. Jafarı and Y. Yaylı, “GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 64, no. 1, pp. 15–27, 2015, doi: 10.1501/Commua1_0000000724.
ISNAD Jafarı, Mehdi - Yaylı, Yusuf. “GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64/1 (February 2015), 15-27. https://doi.org/10.1501/Commua1_0000000724.
JAMA Jafarı M, Yaylı Y. GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64:15–27.
MLA Jafarı, Mehdi and Yusuf Yaylı. “GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 64, no. 1, 2015, pp. 15-27, doi:10.1501/Commua1_0000000724.
Vancouver Jafarı M, Yaylı Y. GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64(1):15-27.

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