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Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.jalgebra.2020.09.017
Rong Tang , Shuai Hou , Yunhe Sheng

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:

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。
更新日期:2021-02-01
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