Geodesic
Necessary and sufficient conditions for a~variety of Leibniz algebras to have polynomial growth
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 207-215.

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We study the behaviour of the codimension sequence of polynomial identities of Leibniz algebras over a field of characteristic 0. We prove that a variety $\mathbf V$ has polynomial growth if and only if the condition $$ \mathbf N_2\mathbf A,\widetilde{\mathbf V_1}\not\subset\mathbf V\subset\widetilde{\mathbf N_c\mathbf A} $$ holds, where $\mathbf N_2\mathbf A$ is the variety of Lie algebras defined by the identity $$ (x_1x_2)(x_3x_4)(x_5x_6)\equiv 0, $$ $\widetilde{\mathbf V_1}$ is the variety of Leibniz algebras defined by the identity $$ x_1(x_2x_3)(x_4x_5)\equiv 0, $$ and $\widetilde{\mathbf N_c\mathbf A}$ is the variety of Leibniz algebras defined by the identity $$ (x_1x_2)\cdots(x_{2c+1}x_{2c+2})\equiv 0. $$ 
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S. P. Mishchenko; O. I. Cherevatenko. Necessary and sufficient conditions for a~variety of Leibniz algebras to have polynomial growth. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 207-215. http://geodesic.mathdoc.fr/item/FPM_2006_12_8_a10/

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