Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras

Guan, Baoling, Chen, Liangyun, and Ma, Yao. "Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras." Czechoslovak Mathematical Journal 64.4 (2014): 1019-1034. <http://eudml.org/doc/269864>.

@article{Guan2014,
abstract = {The paper studies nilpotent $n$-Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for $n$-Lie superalgebras which is a generalization of those for $n$-Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent $n$-Lie superalgebras and obtain several sufficient conditions for an $n$-Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the Jacobson radical.},
author = {Guan, Baoling, Chen, Liangyun, Ma, Yao},
journal = {Czechoslovak Mathematical Journal},
keywords = {nilpotent $n$-Lie superalgebra; Engel’s theorem; $S^\{\ast \}$ algebra; Frattini subalgebra; nilpotent $n$-Lie superalgebra; Engel theorem; Frattini subalgebra},
language = {eng},
number = {4},
pages = {1019-1034},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras},
url = {http://eudml.org/doc/269864},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Guan, Baoling
AU - Chen, Liangyun
AU - Ma, Yao
TI - Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 1019
EP - 1034
AB - The paper studies nilpotent $n$-Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for $n$-Lie superalgebras which is a generalization of those for $n$-Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent $n$-Lie superalgebras and obtain several sufficient conditions for an $n$-Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the Jacobson radical.
LA - eng
KW - nilpotent $n$-Lie superalgebra; Engel’s theorem; $S^{\ast }$ algebra; Frattini subalgebra; nilpotent $n$-Lie superalgebra; Engel theorem; Frattini subalgebra
UR - http://eudml.org/doc/269864
ER -