On some solvable Leibniz algebras and their completeness

The paper is devoted studying solvable Leibniz algebras with a nilradical possessing the codimension equals the number of its generators. We describe this class in non-split nilradical case. Then the case of split nilradical is worked out. We show that the results obtained earlier on this class of Leibniz algebras come as particular cases of the results of this paper. It is shown that such a solvable extension is unique. Finally, we prove that the solvable Leibniz algebras considered are complete.