2023/04/13 by Zhao, Jia, Xu, Senrong, Qiao, Yu
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2304.06324
In this paper, we introduce the notions of relative Rota-Baxter operators of weight 1 on Lie-Yamaguti algebras, and post-\LYA s, which is an underlying algebraic structure of relative Rota-Baxter operators of weight 1. We give the relationship between these two algebraic structures. Besides, we establish the cohomology theory of relative Rota-Baxter operators of weight 1 via the Yamaguti cohomology. Consequently, we use this cohomology to characterize linear deformations of relative Rota-Baxter operators of weight 1 on Lie-Yamaguti algebras. We show that if two linear deformations of a relative Rota-Baxter operator of weight 1 are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, we show that an order n deformation of a relative Rota-Baxter operator of weight 1 can be extended to an order n+1 deformation if and only if the obstruction class in the second cohomology group is trivial.