Geodesic
Decompositions of nilpotent Lie algebras
Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 27-30 
F. M. Malyshev. Decompositions of nilpotent Lie algebras. Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 27-30. http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a1/
@article{MZM_1978_23_1_a1,
     author = {F. M. Malyshev},
     title = {Decompositions of nilpotent {Lie} algebras},
     journal = {Matemati\v{c}eskie zametki},
     pages = {27--30},
     year = {1978},
     volume = {23},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that decompositions of nilpotent Lie algebras are global. In the complex case, nilpotency is also a necessary condition for every decomposition to be global. The results obtained are applied to the classification of complex homogeneous spaces of simply connected nilpotent Lie groups.