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On perfect finite-dimensional Lie algebras, satisfying standard Lie identity of degree 5
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 125-131
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Finite-dimensional Lie algebras satisfying standard Lie identity of degree 5 are considered. A base field $K$ is algebraically closed and of zero characteristic. It is shown that any such algebra can be decomposed into a direct sum of a soluble algebra and a perfect one. It is proved that any such perfect algebra is isomorphic to $A\otimes_Ksl_2$, for a certain commutative and associative $K$-algebra $A$ with unit element, and, thus, satisfies the same identities as Lie algebra $sl_2$. 
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     author = {K. A. Zubrilin and A. Yu. Stepanov},
     title = {On perfect finite-dimensional {Lie} algebras, satisfying standard {Lie} identity of degree 5},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {125--131},
     year = {1996},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/}
}
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K. A. Zubrilin; A. Yu. Stepanov. On perfect finite-dimensional Lie algebras, satisfying standard Lie identity of degree 5. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 125-131. http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/