Abstract
In this paper, first we give the cohomology theory of a 3-Lie algebra with a representation (called a 3- pair) and study the linear deformation theory of a 3- pair. We introduce the notion of a Nijenhuis structure on a 3- pair, which generates a trivial linear deformation. Then by adding compatibility conditions between Nijenhuis structures and relative Rota-Baxter operators, we introduce the notion of a relative Rota-Baxter-Nijenhuis structure on a 3- pair. Finally we construct relative Rota-Baxter-Nijenhuis structures on 3- pairs from those on pairs through certain linear functions.
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