Deformations and the controlling $L_{\infty}$-structure of extended Rota-Baxter Lie algebras
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Yang, Jian
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204954386