Abstract
In this paper, we generalize to n-Lie algebras a corollary of the well-known Engel's theorem which offers some justification for the terminology "nilpotent" and we construct a nilpotent ordinary Lie algebra from a nilpotent n-Lie algebra.
Highlights
In this paper, we generalize to n-Lie algebras a corollary of the well-known Engel’s theorem which offers some justification for the terminology ”nilpotent” and we construct a nilpotent ordinary Lie algebra from a nilpotent n-Lie algebra
The Lie product is taken between n elements of the algebra instead of two
Let G1, G2, ..., Gn be subalgebras of n-Lie algebra G and let {G1, G2, ..., Gn} denote the subspace of G generated by all vectors {x1, x2, ..., xn}, where xi ∈ Gi for i = 1, 2, ..., n
Summary
We generalize to n-Lie algebras a corollary of the well-known Engel’s theorem which offers some justification for the terminology ”nilpotent” and we construct a nilpotent ordinary Lie algebra from a nilpotent n-Lie algebra. Let G1, G2, ..., Gn be subalgebras of n-Lie algebra G and let {G1, G2, ..., Gn} denote the subspace of G generated by all vectors {x1, x2, ..., xn}, where xi ∈ Gi for i = 1, 2, ..., n. Let G be an n-Lie algebra over a field K.
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