Geodesic
Correlation of Poisson Algebras and Lie Algebras in the Language of Identities
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 567-577.

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In the paper, the varieties of Poisson algebras whose ideals of identities contain the identity $\{x,y\}\cdot\{z,t\}=0$ are studied, and the correlation of these varieties with varieties of Lie algebras is investigated. A variety of Poisson algebras of almost exponential growth is presented. An example of a variety of Poisson algebras with fractional exponent is also given.
Mots-clés : Poisson algebra
Keywords: Lie algebra, ideal of identities, variety of algebras, almost exponential growth, Specht variety. 
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S. M. Ratseev. Correlation of Poisson Algebras and Lie Algebras in the Language of Identities. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 567-577. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a7/

[1] S. P. Mishchenko, V. M. Petrogradsky, A. Regev, “Poisson PI algebras”, Trans. Amer. Math. Soc., 359:10 (2007), 4669–4694 | DOI | MR | Zbl

[2] S. M. Ratseev, “Algebry Puassona polinomialnogo rosta”, Sib. matem. zhurn., 54:3 (2013), 700–711 | MR | Zbl

[3] S. M. Ratseev, “Ekvivalentnye usloviya polinomialnosti rosta mnogoobrazii algebr Puassona”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2012, no. 5, 8–13 | MR | Zbl

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

[5] A. N. Krasilnikov, “Konechnaya baziruemost nekotorykh mnogoobrazii algebr Li”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1982, no. 2, 34–38 | MR

[6] S. M. Ratseev, “Konechnaya baziruemost nekotorykh mnogoobrazii algebr Leibnitsa”, Izv. Vuzov. Povolzhskii region, 33:6 (2007), 12–16

[7] S. P. Mischenko, “Nizhnie otsenki razmernostei neprivodimykh predstavlenii simmetricheskikh grupp i pokazatelei eksponenty mnogoobrazii algebr Li”, Matem. sb., 187:1 (1996), 83–94 | DOI | MR | Zbl

[8] S. P. Mischenko, “O mnogoobraziyakh polinomialnogo rosta algebr Li nad polem kharakteristiki nul”, Matem. zametki, 40:6 (1986), 713–721 | MR | Zbl

[9] A. Giambruno, M. Zaicev, “On codimention growth of finitely generated associative algebras”, Adv. Math., 140:2 (1998), 145–155 | DOI | MR | Zbl

[10] A. Giambruno, M. V. Zaicev, “Exponential codimension growth of PI algebras: an exact estimate”, Adv. Math., 142:2 (1999), 221–243 | DOI | MR | Zbl

[11] M. V. Zaicev, S. P. Mishchenko, “An example of a variety of Lie algebras with a fractional exponent”, J. Math. Sci. (New York), 93:6 (1999), 977–982 | DOI | MR | Zbl

[12] A. B. Verevkin, M. V. Zaitsev, S. P. Mischenko, “Dostatochnoe uslovie sovpadeniya nizhnei i verkhnei eksponent mnogoobraziya lineinykh algebr”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2011, no. 2, 86–89 | MR