Geodesic
Cohomologies of parabolic Lie algebras
Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 251-255 
A. K. Tolpygo. Cohomologies of parabolic Lie algebras. Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 251-255. http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a3/
@article{MZM_1972_12_3_a3,
     author = {A. K. Tolpygo},
     title = {Cohomologies of parabolic {Lie} algebras},
     journal = {Matemati\v{c}eskie zametki},
     pages = {251--255},
     year = {1972},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

If $\mathfrak{p}$ is a parabolic subalgebra of a semisimple algebra, the cohomology of $\mathfrak{p}$ is trivial in the associated representation.