AI 中文总结
本文构造Rota-Baxter李代数的同伦余operad，通过代数莫尔斯理论证明其为该李代数operad的极小模型，推导形变复形及其L∞-代数结构，进而提出同伦Rota-Baxter李代数概念。
AI 中文摘要
针对Rota-Baxter李代数，本文构造了一个同伦余operad，利用代数莫尔斯理论证明其余上链构造是Rota-Baxter李代数operad的极小模型。由此推导出Rota-Baxter李代数的形变复形，以及该复形上的L∞-代数结构，进而给出同伦Rota-Baxter李代数的概念。
英文摘要
For Rota-Baxter Lie algebras, a homotopy cooperad is exhibited, whose cobar construction is shown to be the minimal model of the operad of Rota-Baxter Lie algebras by using algebraic Morse theory. The deformation complex of Rota-Baxter Lie algebras as well as the $L_\infty$-algebra structure on this complex are deduced from the minimal model and the notion of homotopy Rota-Baxter Lie algebras is given as a consequence.
