Abstract:
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 $sl_2$.
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