Geodesic
Graded Lie algebras with zero component equal to a sum of commuting ideals
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 511-516 
M. I. Kuznetsov. Graded Lie algebras with zero component equal to a sum of commuting ideals. Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 511-516. http://geodesic.mathdoc.fr/item/SM_1983_44_4_a8/
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     author = {M. I. Kuznetsov},
     title = {Graded {Lie} algebras with zero component equal to a~sum of commuting ideals},
     journal = {Sbornik. Mathematics},
     pages = {511--516},
     year = {1983},
     volume = {44},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_4_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper considers transitive irreducible 1-graded Lie algebras $L=\bigoplus_{i\geqslant-1}L_i$, $L_1=0$, over an algebraically closed field $K$ of characteristic $p\geqslant0$, $p\ne2$. We prove that if $L_0=G_1+\dots+G_s$, $G_i\ne Z(L_0)$, is the decomposition of $L_0$ and the ideals of $G_i$ commute, then $s=1$ or $s=2$. In the latter case $L$ is isomorphic to one of the algebras $A_n$, $A^z_{n_0p-1}$ or $\widetilde{\mathfrak{gl}}(n_0p)=\mathfrak{gl}(n_0p)/\langle1\rangle$. . Bibliography: 7 titles.

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