Classification of (2n-1)-dimensional solvable Leibniz algebras with n-dimensional nilradical

In this article we study solvable Leibniz algebras with abelian nilradicals. The relation between the dimensions of nilradicals and of the corresponding complemented space to the nilradical is estimated. Moreover, we describe (2n - 1)-dimensional solvable Leibniz algebras with n-dimensional nilradical. It is know that the nilradical of these algebras is either n-dimensional abelian algebra or an algebra with one-dimensional square. In addition, the second cohomology groups of the algebras given in the article are computed.

Automated summary

The article studies solvable Leibniz algebras with abelian nilradicals and estimates the relation between the dimensions of nilradicals and their corresponding complemented space. It also describes (2n - 1)-dimensional solvable Leibniz algebras with n-dimensional nilradicals, where the nilradicals are either n-dimensional abelian algebras or algebras with one-dimensional square. Additionally, the second cohomology groups of the algebras discussed in the article are computed.