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arXiv · 2204.13518

Cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights

Shuangjian Guo·Yufei Qin·Kai Wang·Guodong Zhou
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Abstract

This paper is devoted to studying deformation, cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. First we give the notion of a new representation of a Rota-Baxter pre-Lie algebra of arbitrary weight and define the cohomology theory of a Rota-Baxter pre-Lie algebra of arbitrary weight. Then we study formal deformations by lower degree cohomology groups. Finally, we classify abelian extensions of Rota-Baxter pre-Lie algebras of arbitrary weight using the second cohomology group, and classify skeletal Rota-Baxter pre-Lie 2-algebra of arbitrary weight using the third cohomology group as applications.

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BibTeXRIS

Shuangjian Guo, Yufei Qin, Kai Wang, Guodong Zhou. 2022-04-28. Cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. https://arxiv.org/abs/2204.13518

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