Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras
Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras
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DOI：
10.3390/math12010166
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发表时间：
2022-04
期刊：
影响因子：
2.4
通讯作者：
Jia Zhao;Yu Qiao
中科院分区：
文献类型：
--
作者：
Jia Zhao;Yu Qiao
本文利用Yamaguti上同调，建立了Lie-Yamaguti代数上相对Rota-Baxter算子的上同调.然后，我们使用这种类型的上同调的Lie-Yamaguti代数上的相对Rota-Baxter算子的变形的特点。证明了若两个相对Rota-Baxter算子的线性或形式变形等价，则它们的无穷小量在第一上同调群中属于同一上同调类.此外，一个相对Rota-Baxter算子的n阶变形可以推广到n+1阶变形当且仅当第二上同调群中的障碍类是平凡的。
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.