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arXiv · 2310.05360

Maurer-Cartan characterization, $L_\infty$-algebras, and cohomology of relative Rota-Baxter operators on Lie-Yamaguti algebras

Jia Zhao·Yu Qiao
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Abstract

In this paper, we first construct a differential graded Lie algebra that controls deformations of a Lie-Yamaguti algebra. Furthermore, a relative Rota-Baxter operator on a Lie-Yamaguti algebra is characterized as a Maurer-Cartan element in an appropriate $L_\infty$-algebra that we build through the graded Lie bracket of Lie-Yamaguti algebra's controlling algebra, and gives rise to a twisted $L_\infty$-algebra that controls its deformation. Next we establish the cohomology theory of relative Rota-Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then we clarify the relationship between the twisted $L_\infty$-algebra and the cohomology theory. Finally as byproducts, we classify certain deformations on Lie-Yamaguti algebras using the cohomology theory.

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Jia Zhao, Yu Qiao. 2023-10-09. Maurer-Cartan characterization, $L_\infty$-algebras, and cohomology of relative Rota-Baxter operators on Lie-Yamaguti algebras. https://arxiv.org/abs/2310.05360

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