Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms

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, obtain Wells short-exact sequence context algebras. Finally, how these results fit abelian