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.
1
Dept. of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Hamid Darabi; Farshid 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/JOLT_2017_27_1_a14/
@article{JOLT_2017_27_1_a14,
author = {Hamid Darabi and Farshid Saeedi},
title = {On the {Schur} {Multiplier} of {<italic>n</italic>-Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {271--281},
year = {2017},
volume = {27},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a14/}
}
TY - JOUR
AU - Hamid Darabi
AU - Farshid Saeedi
TI - On the Schur Multiplier of n-Lie Algebras
JO - Journal of Lie Theory
PY - 2017
SP - 271
EP - 281
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a14/
ID - JOLT_2017_27_1_a14
ER -
%0 Journal Article
%A Hamid Darabi
%A Farshid Saeedi
%T On the Schur Multiplier of n-Lie Algebras
%J Journal of Lie Theory
%D 2017
%P 271-281
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a14/
%F JOLT_2017_27_1_a14
