Geodesic
On metabelian varieties of Leibniz–Poisson algebras
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 72-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we give algebra constructions that generate the metabelian variety of Leibniz–Poisson algebras with the identity $\{ x, y \} \cdot \{z, t \} = 0$. We give the asymptotic description of the metabelian varieties.
Mots-clés : Poisson algebra, Leibniz–Poisson algebra
Keywords: variety of algebras, growth of variety. 
@article{IIGUM_2013_6_1_a6,
     author = {S. M. Ratseev and O. I. Cherevatenko},
     title = {On metabelian varieties of {Leibniz{\textendash}Poisson} algebras},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {72--77},
     year = {2013},
     volume = {6},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a6/}
}
TY  - JOUR
AU  - S. M. Ratseev
AU  - O. I. Cherevatenko
TI  - On metabelian varieties of Leibniz–Poisson algebras
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2013
SP  - 72
EP  - 77
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a6/
LA  - ru
ID  - IIGUM_2013_6_1_a6
ER  - 
%0 Journal Article
%A S. M. Ratseev
%A O. I. Cherevatenko
%T On metabelian varieties of Leibniz–Poisson algebras
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2013
%P 72-77
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a6/
%G ru
%F IIGUM_2013_6_1_a6
S. M. Ratseev; O. I. Cherevatenko. On metabelian varieties of Leibniz–Poisson algebras. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 72-77. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a6/

[1] E. I. Zelmanov, “Ob engelevykh algebrakh Li”, Sib. mat. zhurn., 29:5 (1988), 112–117 | MR

[2] S. M. Ratseev, “Ekvivalentnye usloviya polinomialnosti rosta mnogoobrazii algebr Puassona”, Vestn. Mosk. un-ta. Ser. 1, Matematika. Mekhanika, 67:5 (2012), 8–13 | MR | Zbl

[3] S. M. Ratseev, “Kommutativnye algebry Leibnitsa–Puassona polinomialnogo rosta”, Vestn. Samar. gos. un-ta. Estestvennonauch. ser., 94:3/1 (2012), 54–65

[4] V. Drensky, G. M. Piacentini Cattaneo, “Varieties of metabelian Leibniz algebras”, J. Algebra and its Applications, 1 (2002), 31–50 | DOI | MR | Zbl