Search

A Rota-Baxter Lie algebra g T 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 g T by another Rota-Baxter Lie algebra h S. We define the non-abelian cohomology H n a b 2 (g T , h S) 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 (h S) × Aut (g T) to be induced by an automorphism in Aut (e U) lies in the cohomology group H n a b 2 (g T , h S). 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. [ABSTRACT FROM AUTHOR]