Geodesic
A property of polarization
Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 453-457 
A. A. Zaitsev. A property of polarization. Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 453-457. http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a1/
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     author = {A. A. Zaitsev},
     title = {A~property of polarization},
     journal = {Matemati\v{c}eskie zametki},
     pages = {453--457},
     year = {1977},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a real Lie group with the Lie algebra $\mathfrak g$, and let f be a real linear functional on $\mathfrak g$. It is established that if $\operatorname{Ker}f$ does not contain nonzero ideals of the algebra $\mathfrak g$, then the existence of a total positive complex polarization for $f$ implies that the Lie algebra of the stationary subgroup of the functional $f$ in $\mathfrak g$ is reductive.