Biderivations of some classes of solvable Leibniz algebras

TL;DR

This paper characterizes anti-derivations and biderivations in certain solvable Leibniz algebras, showing their forms and how they can be used to construct these algebras, with all biderivations being inner in specific cases.

Contribution

It provides a detailed description of anti-derivations and biderivations for null-filiform and filiform Leibniz algebras, including their construction and the fact that all such biderivations are inner.

Findings

Biderivations are explicitly described for null-filiform and filiform Leibniz algebras.

All biderivations in these classes are inner biderivations.

Method to construct Leibniz algebras using these biderivations.

Abstract

In this work, we investigate anti-derivations and biderivation of Leibniz algebras. We describe general form of anti-derivations and biderivations on null-filiform and filiform Leibniz algebras. Moreover, we show how to construct Leibniz algebras, while using these biderivations. We describe general form of anti-derivations and biderivations on solvable Leibniz algebras with null-filiform and filiform nilradicals. Interesting fact that, any biderivations of solvable Leibniz algebras with null-filiform and filiform nilradicals are inner biderivations.