Geodesic
Varieties of Lie algebras with weak growth of the sequence of codimensions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 63-66

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We prove that any variety of Lie algebras with a sequence of codimensions of multilinear identities which grows “weakly”, in particular as a polynomial, is a subvariety in the variety of all Lie algebras whose commutator subalgebra is nilpotent of class at most $c$, for some fixed integer $c$. 
@article{VMUMM_1982_5_a17,
     author = {S. P. Mishchenko},
     title = {Varieties of {Lie} algebras with weak growth of the sequence of codimensions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {63--66},
     publisher = {mathdoc},
     number = {5},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a17/}
}
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S. P. Mishchenko. Varieties of Lie algebras with weak growth of the sequence of codimensions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 63-66. http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a17/