The Decomposition and Uniqueness of $n$-Lie Superalgebras

In this paper, the definitions and some properties of $n$-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional $n$-Lie superalgebras with trivial center. According to the decomposition of $n$-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of $n$-Lie superalgebras, so we can see its application in the decomposition of $n$-Lie superalgebras.