3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras

In this paper, first we introduce the notions of relative Rota-Baxter operators nonzero weight on $3$-Lie algebras and $3$-post-Lie algebras. A 3-post-Lie algebra consists a 3-Lie structure ternary operation such that some compatibility conditions are satisfied. We show operator induces naturally. Conversely, gives rise to new algebra, which is called subadjacent an action original algebra. Then construct $L_\infty$-algebra whose Maurer-Cartan elements weight. Consequently, obtain twisted controls deformations given Finally, cohomology theory for use second group classify infinitesimal deformations.