  In the paper we describe the derivations of two $\mathbb{N}$-graded
infinity-dimensional Lie algebras $\mathbf{n}_1$ and $\mathbf{n}_1$ what are
positive parts of affine Kats-Moody algebras $A^{(1)}_1$ and $A^{(2)}_2$,
respectively. Then we construct all pro-solvable Lie algebras whose potential
nilpotent ideals are $\mathbf{n}_1$ and $\mathbf{n}_2$. For two specific
representatives of these classes low-dimensional (co)homology groups are
computed.

Rings and Algebras