论文标题
lieyrep对上的同时和相对rota-baxter-nijenhuis结构
Cohomology and relative Rota-Baxter-Nijenhuis structures on LieYRep pairs
论文作者
论文摘要
Lieyrep对由一个Lie-Yamaguti代数及其代表组成。在本文中，我们建立了LIEYREP对的共同体学理论，并通过第二个共同体学组来表征它们的线性变形。然后，我们介绍了相对rota-baxter-nijenhuis在lieyrep对，研究其特性的概念，并证明相对rota-baxter-nijenhuis结构在一定条件下产生了一对兼容的相对rota-baxter操作员。最后，我们在lie-yamaguti代数上展示了$ r $ -r $ -Matrix-nijenhuis结构与rota-baxter-nijenhuis结构之间的等价性。
A LieYRep pair consists of a Lie-Yamaguti algebra and its representation. In this paper, we establish the cohomology theory of LieYRep pairs and characterize their linear deformations by the second cohomology group. Then we introduce the notion of relative Rota-Baxter-Nijenhuis structures on LieYRep pairs, investigate their properties, and prove that a relative Rota-Baxter-Nijenhuis structure gives rise to a pair of compatible relative Rota-Baxter operators under a certain condition. Finally, we show the equivalence between $r$-matrix-Nijenhuis structures and Rota-Baxter-Nijenhuis structures on Lie-Yamaguti algebras.
