Generalized Reynolds operators on 3-Lie algebras and NS-3-Lie algebras

In this paper, first we introduce the notion of a twisted Rota-Baxter operator on 3-Lie algebra $\g$ with representation $V$. We show that induces structure $V$, which represents $\g$. By fact, define cohomology and study infinitesimal deformations using second group. Then an NS-3-Lie algebra, produces itself. naturally. Thus algebras can be viewed as underlying algebraic structures operators algebras. Finally Nijenhuis gives rise to deformed 2-cocycle. Consequently, identity map will algebra. also Reynolds serve special case