Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

Abstract

In the paper the class of all solvable extensions of a filiform Leibniz algebra in the infinitedimensional case is classified. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.