@article {
author = {Bai, R. and Gao, Y. and Zhang, Y. and Li, Z.},
title = {Double derivations of n-Lie algebras},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {3},
pages = {897-910},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
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 $ad(L)$.},
keywords = {$n$-Lie algebra,double derivation,derivation,inner derivation},
url = {http://bims.iranjournals.ir/article_980.html},
eprint = {http://bims.iranjournals.ir/article_980_435becbcb5d7a8ea49d428daf9a529cf.pdf}
}