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Split quaternions and semi-Euclidean projective spaces

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  • Ata, Erhan
  • Yayli, Yusuf

Abstract

In this study, we give one-to-one correspondence between the elements of the unit split three-sphere S(3,2) with the complex hyperbolic special unitary matrices SU(2,1). Thus, we express spherical concepts such as meridians of longitude and parallels of latitude on SU(2,1) by using the method given in Toth [Toth G. Glimpses of algebra and geometry. Springer-Verlag; 1998] for S3.

Suggested Citation

  • Ata, Erhan & Yayli, Yusuf, 2009. "Split quaternions and semi-Euclidean projective spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1910-1915.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1910-1915
    DOI: 10.1016/j.chaos.2008.07.049
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    References listed on IDEAS

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    1. El Naschie, M.S., 2005. "Kähler-like manifolds, Weyl spinor particles and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 665-670.
    2. El Naschie, M.S., 2008. "Exceptional Lie groups hierarchy and some fundamental high energy physics equations," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 82-84.
    3. El Naschie, M.S., 2008. "Conformal E-infinity theory, exceptional Lie groups and the elementary particle content of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 216-219.
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    Cited by:

    1. Falcão, M. Irene & Miranda, Fernando & Severino, Ricardo & Soares, M. Joana, 2017. "Basins of attraction for a quadratic coquaternionic map," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 716-724.

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