Cohomologies of modified Rota-Baxter Lie algebras with derivations and applications

B. Imed, B. Sami, N. Saber, S. Mohamed Amin

In this paper, first, we introduce a notion of modified Rota-Baxter Lie algebras of weight λ with derivations (or simply modified Rota-Baxter LieDer pairs) and their representations. Moreover, we investigate cohomologies of a modified Rota-Baxter LieDer pairs with coefficients in a suitable representation. As applications, we study formal one-parameter deformations and abelian extensions of modified Rota-Baxter LieDer pairs. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 189-210