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arXiv · 2609.01304

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

Jian Yang
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Abstract

In this paper, we introduce the controlling $L_{\infty}[1]$-algebra of extended Rota-Baxter algebras. As applications, we obtain the cohomology of extended Rota-Baxter algebras and homotopy extended Rota-Baxter algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we describe the intrinsic relationship among extended Rota-Baxter algebras, extended Rota-Baxter Lie algebras, and the eigenvalues of the extended Rota-Baxter operator. As the generalization of Rota-Baxter algebras with weight and modified Rota-Baxter algebras, the corresponding results also hold for those algebras.

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Jian Yang. 2026-09-01. Deformation theory and the controlling $L_{\infty}$-structure of extended Rota-Baxter algebras. https://arxiv.org/abs/2609.01304

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