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
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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 $sl_2$.
@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},
publisher = {mathdoc},
volume = {2},
number = {1},
year = {1996},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a4/ %G ru %F FPM_1996_2_1_a4
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/