Geodesic
On some varieties of Leibniz–Poisson algebras with extreme properties
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2013), pp. 57-59

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Some varieties of Leibniz–Poisson algebras with extreme properties are presented. We give the least variety of Leibniz–Poisson algebras in which no Leibniz standard identities are valid.
Mots-clés : Poisson algebra, Leibniz–Poisson algebra
Keywords: variety of algebras, growth of a variety. 
S. M. Ratseev; O. I. Cherevatenko. On some varieties of Leibniz–Poisson algebras with extreme properties. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2013), pp. 57-59. http://geodesic.mathdoc.fr/item/VTGU_2013_2_a5/
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[1] Ratseev S. M., “Kommutativnye algebry Leibnitsa–Puassona polinomialnogo rosta”, Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya, 2012, no. 3/1(94), 54–65

[2] Mishchenko S., Valenti A., “A Leibniz variety with almost polynomial growth”, J. Pure Appl. Algebra, 202:1–3 (2005), 82–101 | DOI | MR | Zbl

[3] Abanina L. E., Ratseev S. M., “Mnogoobrazie algebr Leibnitsa, svyazannoe so standartnymi tozhdestvami”, Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya, 2005, no. 6, 36–50 | MR | Zbl

[4] Abanina L. E., Mischenko S. P., “Nekotorye mnogoobraziya algebr Leibnitsa”, Matematicheskie metody i prilozheniya, Trudy Desyatykh matematicheskikh chtenii MGSU, Soyuz, M., 2002, 95–99

[5] Ratseev S. M., “On varieties of Leibniz–Poisson algebras with the identity $\{x,y\}\cdot\{z,t\}=0$”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 97–104