Double derivations of n-Lie algebras
Authors
Abstract:
After introducing double derivations of $n$-Lie algebra $L$ we describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual derivation Lie algebra $mathcal Der(L)$. In particular, we prove that the inner derivation algebra $ad(L)$ is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra with certain constraints on the base field then the centralizer of $ad(L)$ in $mathcal D(L)$ is trivial and $mathcal D(L)$ is centerless. In addition, we obtain that for every perfect $n$-Lie algebra $L$ with zero center, the triple derivations of the derivation algebra $mathcal Der(L)$ are exactly the derivations of $mathcal Der(L)$, and the triple derivations of the inner derivation algebra $ad(L)$ are precisely the derivations of $ad(L)$.
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Journal title
volume 43 issue 3
pages 897- 910
publication date 2017-06-01
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