Geodesic
Representation of the Lorentz transformations in 6-dimensional space-time
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 327 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

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 
@article{KJM_2011_35_2_a10,
     author = {Kostadin Tren\v{c}evski},
     title = {Representation of the {Lorentz} transformations in 6-dimensional space-time},
     journal = {Kragujevac Journal of Mathematics},
     pages = {327 },
     year = {2011},
     volume = {35},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a10/}
}
TY  - JOUR
AU  - Kostadin Trenčevski
TI  - Representation of the Lorentz transformations in 6-dimensional space-time
JO  - Kragujevac Journal of Mathematics
PY  - 2011
SP  - 327 
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a10/
LA  - en
ID  - KJM_2011_35_2_a10
ER  - 
%0 Journal Article
%A Kostadin Trenčevski
%T Representation of the Lorentz transformations in 6-dimensional space-time
%J Kragujevac Journal of Mathematics
%D 2011
%P 327 
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a10/
%G en
%F KJM_2011_35_2_a10
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/