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. 
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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/

[1] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985, 448 pp. | MR | Zbl

[2] Drensky V., Free algebras and PI-algebras. Graduate course in algebra, Springer Verlag, Singapore, 2000, 272 pp. | MR | Zbl

[3] Giambruno A., Zaicev M. V., “On codimention growth of finitely generated associative algebras”, Adv. Math., 140 (1998), 145–155 | DOI | MR | Zbl

[4] Zaitcev M. V., Mishchenko S. P., “Example of variety of Lie algebras with fractional exponent”, J. Math. Sci., 93:6 (1999), 977–982 | DOI | MR

[5] Petrogradsky V. M., “Exponents of subvarieties of upper triangular matrices over arbitrary fields are integral”, Serdika Math., 26:2 (2000), 1001–1010 | MR

[6] Ratseev S. M., “Tozhdestva v mnogoobraziyakh, porozhdennykh algebrami verkhnetreugolnykh matrits”, Sib. matem. zhurn., 52:2 (2011), 416–429 | MR

[7] Maltsev Yu. N., “Bazis tozhdestv algebry verkhnetreugolnykh matrits”, Algebra i logika, 10 (1971), 393–400

[8] Ratseev S. M., “Rost nekotorykh mnogoobrazii algebr Leibnitsa”, Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya, 2006, no. 6(46), 70–77 | MR | Zbl

[9] Ratseev S. M., “Growth of some varieties of Leibniz–Poisson algebras”, Serdica Math. J., 37:4 (2011), 331–340 | MR | Zbl

[10] Ratseev S. M., “Otsenki rosta mnogoobrazii algebr Leibnitsa s nilpotentnym kommutantom”, Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya, 2010, no. 4(78), 65–72

[11] Ratseev S. M., Cherevatenko O. I., “Eksponenty nekotorykh mnogoobrazii algebr Leibnitsa–Puassona”, Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya, 2013, no. 3(104), 42–52