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.

中文翻译：

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Lie 3-代数和3-Lie代数上相关Rota-Baxter算子的变形

摘要 给定一个3-李代数的表示，我们构造了一个李3-代数，其Maurer-Cartan 元素是3-Lie 代数上的相对Rota-Baxter 算子。我们定义了 3-Lie 代数上相对 Rota-Baxter 算子的上同调，通过它我们研究了相对 Rota-Baxter 算子的变形。我们证明，如果 3-Lie 代数上的相对 Rota-Baxter 算子的两个形式变形是等价的，则它们的无穷小在第一上同调群中属于同一上同调类。此外，第二个上同调群中的一个上同调类给出了从 n 阶变形到 n+1 阶变形的可扩展性。