# Some cohomologically rigid solvable Leibniz algebras

## TL;DR

This paper classifies a specific class of solvable Leibniz algebras, proving their uniqueness, centerlessness, and trivial cohomology groups, thus advancing understanding of their structure and rigidity.

## Contribution

It introduces a unique, centerless class of solvable Leibniz algebras with specific quotient properties and establishes their cohomological rigidity.

## Key findings

- The algebra is unique and centerless.
- First and second cohomology groups are trivial.
- Provides structural classification of these Leibniz algebras.

## Abstract

In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first and the second cohomology groups of the algebra with coefficients in itself is trivial.