Geodesic
On exponents of some varieties of linear algebras
Prikladnaâ diskretnaâ matematika, no. 3 (2013), pp. 32-34

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The algebra $UT_s$ of upper triangular matrices of a size $s$ is considered. The equivalent conditions for the growth estimation are obtained for subvarieties in $var(UT_s)$, for varieties of Leibnitz algebras with nilpotent commutant, and for varieties of Leibniz–Poisson algebras with the identities $\{\{x_1,y_1\},\dots,\{x_n,y_n\}\}=0$, $\{x_1,y_1\}\cdot\ldots\cdot\{x_n,y_n\}=0$.
Keywords: variety of linear algebras, growth of a variety, exponent of a variety. 
@article{PDM_2013_3_a3,
     author = {S. M. Ratseev},
     title = {On exponents of some varieties of linear algebras},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {32--34},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_3_a3/}
}
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S. M. Ratseev. On exponents of some varieties of linear algebras. Prikladnaâ diskretnaâ matematika, no. 3 (2013), pp. 32-34. http://geodesic.mathdoc.fr/item/PDM_2013_3_a3/