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This study aims to generalize the notion of compatible Lie algebras to thecompatible Lie Yamaguti algebras. Along with describing the representation ofthe compatible Lie Yamaguti algebra in detail, we also demonstrate thesemi-direct product of this algebra and define the Rota-Baxter operators oncompatible Lie Yamaguti algebras as well as compatible pre-Lie Yamagutialgebras. Using Rota-Baxter operators, we look at how compatible Lie (andcompatible pre-Lie) Yamaguti algebras are related to one another.

On compatible Lie and pre-Lie Yamaguti algebras