Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

TL;DR

This paper classifies all solvable extensions of an infinite-dimensional filiform Leibniz algebra, showing that the second cohomology group of these extensions is trivial, thus advancing understanding of their structure.

Contribution

It provides a complete classification of solvable extensions of infinite-dimensional filiform Leibniz algebras and proves the triviality of their second cohomology group.

Findings

All solvable extensions are classified.

Second cohomology group of extensions is trivial.

Filiform Leibniz algebra is a maximal pro-nilpotent ideal.

Abstract

In the paper the class of all solvable extensions of a filiform Leibniz algebra in the infinite-dimensional 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.