Geodesic
New properties of the Lie algebra variety $\mathbf N_2\mathbf A$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 165-173 
S. P. Mishchenko; Y. R. Fyathutdinova. New properties of the Lie algebra variety $\mathbf N_2\mathbf A$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 165-173. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a8/
@article{FPM_2012_17_7_a8,
     author = {S. P. Mishchenko and Y. R. Fyathutdinova},
     title = {New properties of the {Lie} algebra variety~$\mathbf N_2\mathbf A$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {165--173},
     year = {2012},
     volume = {17},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a8/}
}
TY  - JOUR
AU  - S. P. Mishchenko
AU  - Y. R. Fyathutdinova
TI  - New properties of the Lie algebra variety $\mathbf N_2\mathbf A$
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2012
SP  - 165
EP  - 173
VL  - 17
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a8/
LA  - ru
ID  - FPM_2012_17_7_a8
ER  - 
%0 Journal Article
%A S. P. Mishchenko
%A Y. R. Fyathutdinova
%T New properties of the Lie algebra variety $\mathbf N_2\mathbf A$
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 165-173
%V 17
%N 7
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a8/
%G ru
%F FPM_2012_17_7_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

We continue to consider the properties of the almost polynomial growth variety of Lie algebras over a field of characteristic zero defined by the identity $(x_1x_2)(x_3x_4)(x_5x_6)\equiv0$. Here we have constructed the bases of its multilinear parts and proved the formulas for the colength and codimension sequences of this variety.

[1] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1980 | MR

[2] Maltsev A. I., “Ob algebrakh s tozhdestvennymi opredelyayuschimi sootnosheniyami”, Mat. sb., 26(68):1 (1950), 19–33 | MR | Zbl

[3] Mischenko S. P., “Mnogoobraziya algebr Li s dvustupenno nilpotentnym kommutantom”, Vestsi AN BSSR. Ser. fiz.-mat. nauk, 1987, no. 6, 39–43

[4] Mischenko S. P., “Rost mnogoobrazii algebr Li”, Uspekhi mat. nauk, 45:6(276) (1990), 25–45 | MR | Zbl

[5] Giambruno A., Zaicev M., Polynomial Identities and Asymptotic Methods, Math. Surveys Monographs, 122, Amer. Math. Soc., Providence, 2005 | DOI | MR | Zbl