Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 27 (2017), No. 1, 271--281Copyright 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 [ Fulltext-pdf  (257  KB)] for subscribers only.