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arXiv · 2608.29829

Deformations and the controlling $L_{\infty}$-structure of extended Rota-Baxter Lie algebras

Jian Yang
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Abstract

In this paper, we introduce the controlling $L_{\infty}[1]$-algebra of extended Rota-Baxter Lie algebras. As applications, we obtain the cohomology of extended Rota-Baxter Lie algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we get the notion of homotopy extended Rota-Baxter Lie algebras. Specifically, we present the controlling $L_{\infty}[1]$-algebra of modified Rota-Baxter Lie algebras and of Rota-Baxter Lie algebras with weight.

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Jian Yang. 2026-08-30. Deformations and the controlling $L_{\infty}$-structure of extended Rota-Baxter Lie algebras. https://arxiv.org/abs/2608.29829

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