Abstract
A Rota-Baxter Lie algebra gT is a Lie algebra g equipped with a Rota-Baxter operator T:g→g. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra gT by another Rota-Baxter Lie algebra hS. We define the non-abelian cohomology Hnab2(gT,hS) which classifies equivalence classes of such extensions. Given a non-abelian extension [Display omitted] of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of Rota-Baxter automorphisms in Aut(hS)×Aut(gT) to be induced by an automorphism in Aut(eU) lies in the cohomology group Hnab2(gT,hS). As a byproduct, we obtain the Wells short-exact sequence in the context of Rota-Baxter Lie algebras. Finally, we show how these results fit with abelian extensions of Rota-Baxter Lie algebras.
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