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Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 1019-1034 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-014-0150-5
Classification : 17A42, 17A70, 17B45, 17B50
Keywords: nilpotent $n$-Lie superalgebra; Engel's theorem; $S^{\ast }$ algebra; Frattini subalgebra 
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Guan, Baoling; Chen, Liangyun; Ma, Yao. Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 1019-1034. doi: 10.1007/s10587-014-0150-5

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