Classification of solvable Leibniz algebras with null-filiform nilradical

Abstract

In this paper we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals, and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra, as well.