On pro-solvable Lie algebras with maximal pro-nilpotent ideals $\mathfrak{m}_0$ and $\mathfrak{m}_2$

Abstract: The paper is devoted to the study of pro-solvable Lie algebras whose maximal pro-nilpotent ideal is either $\mathfrak{m}_0$ or $\mathfrak{m}_2$. Namely, we describe such Lie algebras and establish their completeness. Triviality of the second cohomology group for one of the obtained algebra is established.