Geodesic
Codimensions of varieties of Poisson algebras with Lie nilpotent commutants
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 241-244

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We study varieties of Poisson algebras defined by the identities $\{x_1,x_2\}\cdot\{x_3,x_4\}=0$ and $\{\{x_1,x_2\},\ldots,\{x_{2s+1}, x_{2s+2}\}\}=0$, $s\geq 1$. For each of the varieties we find a carrier algebra and build a basis of the $n$th proper polylinear space. We derive exact formulas for exponential generating functions for sequences of codimensions and proper codimensions as well as exact formulas for codimensions and proper codimensions.
Mots-clés : Poisson algebra
Keywords: variety of algebras, growth of a variety. 
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     title = {Codimensions of varieties of {Poisson} algebras with {Lie} nilpotent commutants},
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S. M. Ratseev; O. I. Cherevatenko. Codimensions of varieties of Poisson algebras with Lie nilpotent commutants. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 241-244. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a22/