Geodesic
On the Schur Multiplier of n-Lie Algebras
Journal of Lie theory, Tome 27 (2017) no. 1, pp. 271-281
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We give the structure of all covers of $n$-Lie algebras with finite dimensional Schur multipliers, which generalizes an earlier work of Salemkar et al. Also, for an $n$-Lie algebra $A$ of dimension $d$, we find the upper bound $\dim{\cal M}(A) \leq{d\choose n}$, where ${\cal M}(A)$ denotes the Schur multiplier of $A$ and that the equality holds if and only if $A$ is abelian. Finally, we give a formula for the dimension of the Schur multiplier of the direct sum of two $n$-Lie algebras.
Classification : 17B05, 17B30
Mots-clés : n-Lie algebra, covering n-Lie algebra, isoclinism, Schur multiplier 
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     author = {H. Darabi and F. Saeedi},
     title = {On the {Schur} {Multiplier} of {\protect\emph{n}-Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {271--281},
     year = {2017},
     volume = {27},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_1_JLT_2017_27_1_a14/}
}
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H. Darabi; F. Saeedi. On the Schur Multiplier of n-Lie Algebras. Journal of Lie theory, Tome 27 (2017) no. 1, pp. 271-281. http://geodesic.mathdoc.fr/item/JLT_2017_27_1_JLT_2017_27_1_a14/