Geodesic
Central polynomials for adjoint representations of simple Lie algebras exist
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1015-1025 
A. A. Kagarmanov; Yu. P. Razmyslov. Central polynomials for adjoint representations of simple Lie algebras exist. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1015-1025. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a4/
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     author = {A. A. Kagarmanov and Yu. P. Razmyslov},
     title = {Central polynomials for adjoint representations of simple {Lie} algebras exist},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1015--1025},
     year = {1999},
     volume = {5},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Yu. P. Razmyslov has proved that for any finite dimensional reductive Lie algebra $\mathcal G$ over a field $K$ of zero characteristic ($\dim_{K}\mathcal G=m$) and for its arbitrary associative enveloping algebra $U$ with non-empty center $Z(U)$ there exists a central polynomial which is multilinear and skew-symmetric in $k$ sets of $m$ variables for a certain positive integer $k$. This result is now proved for adjoint representations of classical simple Lie algebras of type $A_s,B_s,C_s,D_s$ and matrix Lie algebra $M_n$ over fields of positive characteristic.