Biderivations of some classes of solvable Leibniz algebras

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.