Abstract
3-Lie-Rinehart algebras are an algebraic axiomatization of the basic properties of Filippov algebroids (for n = 3). The purpose of this paper is to introduce the notion of relative Rota-Baxter operators on a 3-Lie-Rinehart algebra and give some classical characterizations. Next, we define 3-pre-Lie-Rinehart algebras which can be seen as a dendrification of 3-Lie-Rinehart algebras by means of relative Rota-Baxter operators. Moreover, we introduce the notion of trace functions on Lie-Rinehart algebra and pre-Lie-Rinehart algebra to construct their induced 3-Lie-Rinehart algebra and 3-pre-Lie-Rinehart algebra, respectively.
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