Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 125-131
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K. A. Zubrilin; A. Yu. Stepanov. On perfect finite-dimensional Lie algebras, satisfying standard Lie identity of degree 5. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 125-131. http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/
@article{FPM_1996_2_1_a4,
author = {K. A. Zubrilin and A. Yu. Stepanov},
title = {On perfect finite-dimensional {Lie} algebras, satisfying standard {Lie} identity of degree 5},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {125--131},
year = {1996},
volume = {2},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/}
}
TY - JOUR
AU - K. A. Zubrilin
AU - A. Yu. Stepanov
TI - On perfect finite-dimensional Lie algebras, satisfying standard Lie identity of degree 5
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1996
SP - 125
EP - 131
VL - 2
IS - 1
UR - http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/
LA - ru
ID - FPM_1996_2_1_a4
ER -
%0 Journal Article
%A K. A. Zubrilin
%A A. Yu. Stepanov
%T On perfect finite-dimensional Lie algebras, satisfying standard Lie identity of degree 5
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1996
%P 125-131
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/
%G ru
%F FPM_1996_2_1_a4
Finite-dimensional Lie algebras satisfying standard Lie identity of degree 5 are considered. A base field $K$ is algebraically closed and of zero characteristic. It is shown that any such algebra can be decomposed into a direct sum of a soluble algebra and a perfect one. It is proved that any such perfect algebra is isomorphic to $A\otimes_Ksl_2$, for a certain commutative and associative $K$-algebra $A$ with unit element, and, thus, satisfies the same identities as Lie algebra $sl_2$.
