Some characterizations of nilpotent $n$-Lie superalgebras

TL;DR

This paper investigates the structure of nilpotent n-Lie superalgebras, proving Engel's theorem for them, exploring their properties, and providing conditions for their nilpotency.

Contribution

It introduces Engel's theorem for n-Lie superalgebras and offers new criteria to determine their nilpotency.

Findings

Proved Engel's theorem for n-Lie superalgebras

Identified properties of nilpotent n-Lie superalgebras

Provided sufficient conditions for nilpotency

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.