论文标题
在Lie-Yamaguti代数上相对Rota-Baxter操作员的同时和变形
Cohomology and deformations of Relative Rota-Baxter operators on Lie-Yamaguti algebras
论文作者
论文摘要
在本文中，我们通过Yamaguti的同学建立了相对Rota-Baxter操作员在lie-Yamaguti代数上的共同体。然后，我们使用这种类型的共同体来表征lie-yamaguti代数上相对Rota-Baxter操作员的变形。我们表明，如果相对Rota-Baxter操作员的两个线性或形式变形等效，那么它们的无限次数在第一个共同体学组中是相同的共同体学类别。此外，当且仅当第二个同胞组中的阻塞类是微不足道的情况下，只有当时，只有当时，只有当时，只有当时，只有当时，只有当时，相对rota-baxter操作员的订单$ n $变形可以扩展到$ n+1 $变形的订单。
In this paper, we establish the cohomology of relative Rota-Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then we use this type of cohomology to characterize deformations of relative Rota-Baxter operators on Lie-Yamaguti algebras. We show that if two linear or formal deformations of a relative Rota-Baxter operator are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, an order $n$ deformation of a relative Rota-Baxter operator can be extended to an order $n+1$ deformation if and only if the obstruction class in the second cohomology group is trivial.
