Geodesic
Simple Lie algebras satisfying the standard Lie identity of degree~5
Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 553-590

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A description is given of simple Lie algebras over fields of characteristic different from two that satisfy the identity $$ \sum_{\sigma\in S_4}\operatorname{sgn}(\sigma)[z,x_{\sigma(1)},x_{\sigma(2)},x_{\sigma(3)},x_{\sigma(4)}]=0. $$ Bibliography: 14 titles. 
@article{IM2_1986_26_3_a4,
     author = {Yu. P. Razmyslov},
     title = {Simple {Lie} algebras satisfying the standard {Lie} identity of degree~5},
     journal = {Izvestiya. Mathematics },
     pages = {553--590},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a4/}
}
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Yu. P. Razmyslov. Simple Lie algebras satisfying the standard Lie identity of degree~5. Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 553-590. http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a4/