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 [Formula: see text]-Lie algebras and provide some examples. Next, we give various constructions of modified Rota–Baxter operators of nonzero weight according to constructions of [Formula: see text]-Lie algebras. Furthermore, we define a cohomology of modified Rota–Baxter operators of nonzero weight on [Formula: see text]-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 [Formula: see text]-algebra structures whose Maurer–Cartan elements correspond to relative and absolute modified Rota–Baxter [Formula: see text]-Lie algebra structures of nonzero weight, respectively. Lastly, we compare our [Formula: see text]-algebraic approach with the deformation-controlling [Formula: see text]-algebra for relative Rota–Baxter [Formula: see text]-Lie operators developed by Hou, Sheng, and Zhou.