Geodesic
Local decompositions of pseudo-orthogonal groups
Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 633-643

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We find all the local decompositions of the Lie algebra $\mathfrak{so}(1,n+1)$ in the sum of two Lie subal-gebras. We also find all the connected transitive subgroups in the conformai group of Euclidean space, the transitive subgroup is either contained in the group of motions or contains the group of displacements. 
@article{MZM_1974_16_4_a16,
     author = {F. M. Malyshev},
     title = {Local decompositions of pseudo-orthogonal groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {633--643},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a16/}
}
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F. M. Malyshev. Local decompositions of pseudo-orthogonal groups. Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 633-643. http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a16/