Geodesic
The Engel identity and its application
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 419-426

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

In the case of characteristic zero, the Engel identity implies nilpotence in the variety generated by simple infinite-dimensional Lie algebras of Cartan type. An analogous result is also true for 2-metabelian Lie algebras (an algebra is called 2-metabelian if every 2-generator subalgebra is metabelian) over a field whose characteristic does not divide $5!\,$, which in this case permits one to prove solvability of the variety of 2-metabelian Lie algebras. Bibliography: 10 titles. 
@article{SM_1984_49_2_a8,
     author = {S. P. Mishchenko},
     title = {The {Engel} identity and its application},
     journal = {Sbornik. Mathematics},
     pages = {419--426},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_2_a8/}
}
TY  - JOUR
AU  - S. P. Mishchenko
TI  - The Engel identity and its application
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 419
EP  - 426
VL  - 49
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1984_49_2_a8/
LA  - en
ID  - SM_1984_49_2_a8
ER  - 
%0 Journal Article
%A S. P. Mishchenko
%T The Engel identity and its application
%J Sbornik. Mathematics
%D 1984
%P 419-426
%V 49
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1984_49_2_a8/
%G en
%F SM_1984_49_2_a8
S. P. Mishchenko. The Engel identity and its application. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 419-426. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a8/