$(\sigma ,\sigma )$- $n$-derivations of 3-Lie algebras

In this paper, drawing on the classical theory of skew $n$-derivations on prime and semiprime rings, we generalize the concept of $(\sigma ,\sigma )$-derivations to the framework of 3-Lie algebras and introduce the notion of $(\sigma ,\sigma )$- $n$-derivations. Subsequently, several fundamental properties of $(\sigma ,\sigma )$- $n$-derivations on 3-Lie algebras are established. Furthermore, we prove that the $(\sigma ,\sigma )$-derivation space of any non-abelian 3-dimensional 3-Lie algebra is 6-dimensional, providing a precise dimensional characterization for the low-dimensional case.