Cohomologies and Wells exact sequences of Rota–Baxter Lie–Yamaguti algebras

In the present paper, first we introduce the notion of a Rota–Baxter Lie–Yamaguti algebra and its representation. Second, we develop cohomologies of Rota–Baxter Lie–Yamaguti algebras with any weight. Finally, we investigate the inducibility of pairs of Rota–Baxter Lie–Yamaguti algebra automorphisms and derive the Wells exact sequences about abelian extensions of Rota–Baxter Lie–Yamaguti algebras.