Geodesic
On types of overexponential growth in Lie PI-algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 989-1007

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The growth function of identities $c_n(\mathcal{V})$ for varieties of Lie algebras is studied; where $c_n(\mathcal{V})$ is the dimension of a linear span of multilinear words in $n$ distinct letters in a free algebra $F(\mathcal{V},X)$ of the variety $\mathcal{V}$. The main results are as follows: the description of types of overexponential growth is suggested; the growth of identities for polynilpotent varieties is found. A complexity function $\mathcal{C}(\mathcal{V},z)$ is used; it corresponds to any nontrivial variety of Lie algebras $\mathcal{V}$ and is an entire function of a complex variable. 
@article{FPM_1995_1_4_a9,
     author = {V. M. Petrogradsky},
     title = {On types of overexponential growth in {Lie} {PI-algebras}},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {989--1007},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a9/}
}
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V. M. Petrogradsky. On types of overexponential growth in Lie PI-algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 989-1007. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a9/