发表机构
School of Mathematical Sciences, East China Normal University（华东师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入扩张Rota-Baxter李代数的控制$L_{\infty}[1]$-代数，应用其得到该类代数的上同调，研究其阿贝尔扩张、形式形变及同伦版本的相关概念。
AI 中文摘要
本文引入扩张Rota-Baxter李代数的控制$L_{\infty}[1]$-代数，作为应用得到扩张Rota-Baxter李代数的上同调；还利用低阶上同调群研究阿贝尔扩张与形式形变，最后给出同伦扩张Rota-Baxter李代数的概念，具体呈现了修正Rota-Baxter李代数及带权Rota-Baxter李代数的控制$L_{\infty}[1]$-代数。
英文摘要
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.
Comments34 pages
