On some classes of 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 up to isomorphism. 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. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper is devoted to the study of solvable Leibniz algebras with a nilradical possessing the same dimension as the number of its generators. The class of such algebras is described up to isomorphism in the non-split nilradical case, and then the case of split nilradical is worked out. It is shown that the earlier results on this class of Leibniz algebras are particular cases of the results obtained in this paper. Furthermore, it is proven that such a solvable extension is unique, and the solvable Leibniz algebras considered in this study are complete.