Journal of Lie Theory

no. 1
On the Schur Multiplier of n-Lie Algebras
Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 271-281
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.
DOI: 10.5802/jolt.945
Classification: 17B05, 17B30
Keywords: n-Lie algebra, covering n-Lie algebra, isoclinism, Schur multiplier 
@article{JOLT_2017_27_1_a14,
     author = {H. Darabi and F. Saeedi},
     title = {On the {Schur} {Multiplier} of {n-Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {271--281},
     year = {2017},
     volume = {27},
     number = {1},
     doi = {10.5802/jolt.945},
     zbl = {1375.17004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.945/}
}
TY  - JOUR
AU  - H. Darabi
AU  - F. 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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.945/
DO  - 10.5802/jolt.945
ID  - JOLT_2017_27_1_a14
ER  - 
%0 Journal Article
%A H. Darabi
%A F. 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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.945/
%R 10.5802/jolt.945
%F JOLT_2017_27_1_a14
H. Darabi; F. Saeedi. On the Schur Multiplier of n-Lie Algebras. Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 271-281. doi: 10.5802/jolt.945

Cited by Sources: