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 pronilpotent ideal is either m 0 or 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.

On derivations and low-dimensional (co)homology groups of pro-sovable Lie algebras associated with $\mathbf{n}_1$ and $\mathbf{n}_2$

“…The algebras n 1 and n 2 are two representatives (among a few others) of the isomorphism classes of natural graded algebras over fields of characteristic zero given by A. Fialowski and D.Millionshchikov (see [3,9]). Note that the similar problems that in this paper for another two representative denoted by the authors of [3,9] as m 0 and m 2 have been treated earlier in [1].…”