Modified Rota–Baxter operators of nonzero weight on 3-Lie algebras

In this paper, we introduce the notion of modified Rota–Baxter operators of nonzero weight on 3-Lie algebras and provide some examples. Next, we give various constructions of modified Rota–Baxter operators of nonzero weight according to constructions of 3-Lie algebras. Furthermore, we define a cohomology of modified Rota–Baxter operators of nonzero weight on 3-Lie algebras with coefficients in a suitable representation. As an application, we study formal deformations of modified Rota–Baxter operators of nonzero weight that are generated by the above-defined cohomology. In the final part of the paper, we construct two L_∞[1]-algebra structures whose Maurer–Cartan elements correspond to relative and absolute modified Rota–Baxter 3-Lie algebra structures of nonzero weight, respectively. Lastly, we compare our L_∞[1]-algebraic approach with the deformation-controlling L_∞[1]-algebra for relative Rota–Baxter 3-Lie operators developed by Hou, Sheng, and Zhou.