Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras

Abstract

Abstract Given a representation of a 3-Lie algebra, we construct a Lie 3-algebra, whose Maurer-Cartan elements are relative Rota-Baxter operators on the 3-Lie algebra. We define the cohomology of relative Rota-Baxter operators on 3-Lie algebras, by which we study deformations of relative Rota-Baxter operators. We show that if two formal deformations of a relative Rota-Baxter operator on a 3-Lie algebra are equivalent, then their infinitesimals are in the same cohomological class in the first cohomology group. Moreover, the extendability of an order n deformation to an order n + 1 deformation is given by a cohomology class in the second cohomology group.