Geodesic
Exponents of some varieties of Leibniz–Poisson algebras
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2013), pp. 42-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper equivalent conditions for the estimation of growth of varieties of Leibniz–Poisson algebras with nilpotent commutant are received.
Mots-clés : Poisson algebra, Leibniz–Poisson algebra
Keywords: variety of algebras, growth of a variety. 
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S. M. Ratseev; O. I. Cherevatenko. Exponents of some varieties of Leibniz–Poisson algebras. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2013), pp. 42-52. http://geodesic.mathdoc.fr/item/VSGU_2013_3_a4/

[1] Ratseev S. M., “Kommutativnye algebry Leibnitsa–Puassona polinomialnogo rosta”, Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya, 2012, no. 3/1(94), 54–65

[2] Regev A., “Existence of polynomial identities in $A\otimes B$”, Bull. Amer. Math. Soc., 77:6 (1971), 1067–1069 | DOI | 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] Giambruno A., Zaicev M. V., “Exponential codimension growth of P.I. algebras: an exact estimate”, Adv. Math., 142 (1999), 221–243 | DOI | MR | Zbl

[5] Volichenko I. B., “Mnogoobrazie algebr Li s tozhdestvom $[[x_1,x_2,x_3],[x_4,x_5,x_6]] = 0$ nad polem kharakteristiki nul”, Sib. matem. zhurnal, 25:3 (1984), 40–54 | Zbl

[6] Mishchenko S. P., Zaicev M. V., “An example of a variety of Lie algebras with a fractional exponent”, Journal of Mathematical Sciences, 93:6 (1999), 977–982 | DOI | MR | Zbl

[7] Ratseev S. M., “O mnogoobraziyakh algebr Puassona polinomialnogo rosta”, Algebra i matematicheskaya logika, Materialy mezhdunarodnoi konferentsii, posvyaschennoi 100-letiyu so dnya rozhdeniya professora V. V. Morozova, KFU, Kazan, 2011, 156–157 | Zbl

[8] Ratseev S. M., “O mnogoobrazii algebr Puassona s tozhdestvom $\{x_1, x_2\}\times \{x_3, x_4\}=0$”, Algebry Li, algebraicheskie gruppy i teoriya invariantov, Tez. dokl. 3 mezhdunar. shkoly-konf. (Tolyatti, 2012), 43–45

[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., “Rost v algebrakh Puassona”, Algebra i logika, 50:1 (2011), 68–88 | MR

[12] Ratseev S. M., “Tozhdestva v mnogoobraziyakh, porozhdennykh algebrami verkhnetreugolnykh matrits”, Sibirskii matematicheskii zhurnal, 52:2 (2011), 416–429 | MR | Zbl