A Rota-Baxter Lie algebra gTβ is a Lie algebra g
equipped with a Rota-Baxter operator T:gβg. In this paper, we consider non-abelian extensions of a
Rota-Baxter Lie algebra gTβ by another Rota-Baxter Lie algebra
hSβ. We define the non-abelian cohomology Hnab2β(gTβ,hSβ) which classifies {equivalence classes of}
such extensions. Given a non-abelian extension 0βhSβiβeUβpβgTββ0
of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of
Rota-Baxter automorphisms in Aut(hSβ)ΓAut(gTβ) to be induced by an automorphism in
Aut(eUβ) lies in the cohomology group Hnab2β(gTβ,hSβ). As a byproduct, we obtain the Wells
short-exact sequence in the context of Rota-Baxter Lie algebras.Comment: Any comments/suggestions are welcom