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

In this paper, we consider compatible Hom-Lie algebras as a twisted version of Lie algebras. Compatible are characterized Maurer-Cartan elements in suitable bidifferential graded algebra. We also define cohomology theory for generalizing the recent work Liu, Sheng and Bai. As applications cohomology, study abelian extensions deformations