Maurer–Cartan Characterization, Cohomology and Deformation of Compatible Lie Yamaguti Algebras

This study aims to generalize the notion of compatible Lie algebras to compatible Lie Yamaguti algebras. Along with describing the representation of the compatible Lie Yamaguti algebra in detail, we also introduce the Maurer–Cartan characterization and cohomology of compatible Lie Yamaguti algebras. As an application of the obtained cohomology, we study its infinitesimal deformations. We define Rota–Baxter operators on compatible Lie Yamaguti algebras as well as on compatible pre-Lie Yamaguti algebras. Using Rota–Baxter operators, we examine how compatible Lie (and compatible pre-Lie) Yamaguti algebras are related.