*主持人：周国栋 教授

*讲座内容简介：
In this talk, we establish the cohomology of the relative Rota-Baxter operators on Lie-Yamaguti algebras using the Yamaguti cohomology. Then we use this type of cohomology to characterize the deformations of the 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 cohomological classes 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.

*主讲人简介：
赵嘉，2021年12月获得吉林大学理学博士学位，在读期间师从生云鹤教授。2022年3月至今，任职南通大学理学院讲师职位。主要从事Lie-Yamaguti代数及其相对罗巴算子的形变和上同调的研究。