Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras

Abstract

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.

Keywords

• Lie-Yamaguti algebra
• relative Rota–Baxter operator
• cohomology
• deformation