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代数的控制$L_{\infty}[1]$-代数，应用其得到该类代数的上同调、同伦代数，研究阿贝尔扩张与形式形变，阐明其与扩张Rota-Baxter李代数等的联系，相关结果也适用于两类推广的Rota-Baxter代数。
AI 中文摘要
本文引入扩张Rota-Baxter代数的控制$L_{\infty}[1]$-代数。作为应用，我们得到扩张Rota-Baxter代数的上同调与同伦扩张Rota-Baxter代数；还通过低阶上同调群研究阿贝尔扩张与形式形变；最后阐明扩张Rota-Baxter代数、扩张Rota-Baxter李代数及扩张Rota-Baxter算子本征值间的内在联系。作为带权Rota-Baxter代数与修正Rota-Baxter代数的推广，相关结果也适用于这些代数。
英文摘要
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.
Comments36 pages
