Geodesic
Representation of the Lorentz transformations in 6-dimensional space-time
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 327 .

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In this paper we consider first the space-time as a principal bundle with structure group $SO(3,{\mathbb C})$ over the base $B={\mathbb R}^3$. From this viewpoint the 4-vector of velocity is replaced now by a $3\times 3$ orthogonal Hermitian matrix. Starting from the structure group $SO(3,{\mathbb C})$ the Lorentz transformations are written in 6 dimensions. Further it is considered a more sophisticated model of space-time with the same structural group $SO(3,{\mathbb C})$ over the base $SO(3,{\mathbb R})$. In this model there are only rotations, but no translations. So the Lorentz transformations are also converted for this bundle.
Classification : 83A05 83F05 22E60
Keywords: Lorentz transformations, Space-time, Cosmological model 
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Kostadin Trenčevski. Representation of the Lorentz transformations in 6-dimensional space-time. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 327 . http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a10/