Geodesic
On subvariety of variety generated by a simple infinite Lie algebra of Cartan type general series $W_2$
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 125-129 
O. A. Bogdanchuk. On subvariety of variety generated by a simple infinite Lie algebra of Cartan type general series $W_2$. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 125-129. http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a0/
@article{ISU_2014_14_2_a0,
     author = {O. A. Bogdanchuk},
     title = {On subvariety of variety generated by a~simple infinite {Lie} algebra of {Cartan} type general series~$W_2$},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {125--129},
     year = {2014},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a0/}
}
TY  - JOUR
AU  - O. A. Bogdanchuk
TI  - On subvariety of variety generated by a simple infinite Lie algebra of Cartan type general series $W_2$
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 125
EP  - 129
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a0/
LA  - ru
ID  - ISU_2014_14_2_a0
ER  - 
%0 Journal Article
%A O. A. Bogdanchuk
%T On subvariety of variety generated by a simple infinite Lie algebra of Cartan type general series $W_2$
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 125-129
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a0/
%G ru
%F ISU_2014_14_2_a0

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

We consider numerical characteristics of Lie algebras variety over a field of characteristic zero, basically, the exponent of variety. Here, was constructed the infinite series of varieties of Lie algebras with different fractional exponents, which belong to variety generated by a simple infinite Lie algebra of Cartan type general series $W_2$.

[1] Bakhturin Iu. A, Identities in Lie algebras, Nauka, Moscow, 1985, 448 pp. | MR | Zbl

[2] Giambruno A., Zaicev M., Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, 122, American Math. Soc., Providence, RI, 2005, 352 pp. | DOI | MR | Zbl

[3] Mishchenko S. S., “New example of a variety of Lie algebras with fractional exponent”, Moscow Univ. Math. Bull., 66 (2011), 264–266 | DOI | MR

[4] Kirillov A. A., Molev A. I., On the algebraic structure of the Lie algebra of vector fields, Preprint No 16, In-t prikl. matematiki im. M. V. Keldysha AN SSSR, Moscow, 1985, 23 pp.

[5] Malyusheva O. A., Mishchenko S. P., Verevkin A. B., “Series of varieties of Lie algebras of different fractional exponents”, Compt. rend. Acad. Bulg. Sci., 66:3 (2013), 321–330 | MR