Journal of Lie Theory 27 (2017), No. 1, 271--281
Copyright Heldermann Verlag 2017
On the Schur Multiplier of n-Lie Algebras
Hamid Darabi
Dept. of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
darabi@iauesf.ac.ir
Farshid Saeedi
Dept. of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
saeedi@mshdiau.ac.ir
[Abstract-pdf]
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.
Keywords: n-Lie algebra, covering n-Lie algebra, isoclinism, Schur multiplier.
MSC: 17B05; 17B30
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