Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

Jun Jiang; Yunhe Sheng

doi:10.1016/j.jalgebra.2022.03.027

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arXiv · 2108.08294

Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

Jun Jiang·Yunhe Sheng

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Abstract

In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian extensions of relative Rota-Baxter Lie algebras using the second cohomology group, and classify skeletal relative Rota-Baxter Lie 2-algebras using the third cohomology group as applications. At last, using the established general framework of representations and cohomologies of relative Rota-Baxter Lie algebras, we give the notion of representations of Rota-Baxter Lie algebras, which is consistent with representations of Rota-Baxter associative algebras in the literature, and introduce the cohomologies of Rota-Baxter Lie algebras with coefficients in a representation. Applications are also given to classify abelian extensions of Rota-Baxter Lie algebras and skeletal Rota-Baxter Lie 2-algebras.

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BibTeX RIS

Jun Jiang, Yunhe Sheng. 2021-08-16. Representations and cohomologies of relative Rota-Baxter Lie algebras and applications. https://doi.org/10.1016/j.jalgebra.2022.03.027

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