Sur les triples de Manin pour les alg\`ebres de Lie r\'eductives complexes

We study Manin triples for a reductive Lie algebra, $\text{g}$. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf. KAROLINSKY E., {\em A Classification of Poisson homogeneous spaces of a compact Poisson Lie group}, Dokl. Ak. Nauk, 359 (1998), 13-15). Then we show that, if $\text{g}$ is non commutative, one can attach, to each Manin triple in $\text{g}$, an other one for a strictly smaller reductive complex Lie subalgebra of $\text{g}$. We study also the inverse process.