(σ, σ)n-derivations of 3-Lie algebras

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Abstract

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

Keywords

3-Lie algebra / automorphism / (σ, σ)-n-derivation / matrix representation

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