Geodesic
Squares of adjoint endomorphisms in simple Lie $p$-algebras
Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 435-473

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A new characterization of simple Lie $p$-algebras of classical type based on the properties of nilpotent elements is given herein. By this means an analogy is also established between degenerate Lie algebras of a special class and infinite Lie algebras of zero characteristic. 
@article{IM2_1967_1_2_a14,
     author = {A. I. Kostrikin},
     title = {Squares of adjoint endomorphisms in simple {Lie} $p$-algebras},
     journal = {Izvestiya. Mathematics },
     pages = {435--473},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a14/}
}
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A. I. Kostrikin. Squares of adjoint endomorphisms in simple Lie $p$-algebras. Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 435-473. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a14/