
Journal of Lie Theory 27 (2017), No. 1, 271281 Copyright Heldermann Verlag 2017 On the Schur Multiplier of nLie 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 [Abstractpdf] 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: nLie algebra, covering nLie algebra, isoclinism, Schur multiplier. MSC: 17B05; 17B30 [ Fulltextpdf (257 KB)] for subscribers only. 