Some characterizations of nilpotent $n$-Lie superalgebras

Abstract

The paper studies nilpotent $n$-Lie superalgebras. More specifically speaking, we first prove Engel's theorem for $n$-Lie superalgebras. Second, we research some properties of nilpotent $n$-Lie superalgebras, Finally, we give several sufficient conditions that an $n$-Lie superalgebra is nilpotent.