Search

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded p-filiform non-Lie Leibniz algebra (n − p ≥ 4) and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras. [ABSTRACT FROM AUTHOR]

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself. [ABSTRACT FROM AUTHOR]

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $$sl_2^1\oplus sl_2^2\oplus \dots \oplus sl_2^s\oplus R,$$ where R is a solvable radical. The classifications of such Leibniz algebras in the cases $$\mathrm{dim} R=2, 3$$ and $$\mathrm{dim} I\ne 3$$ have been obtained. Moreover, we classify Leibniz algebras with $$L/I\cong sl_2^1\oplus sl_2^2$$ and some conditions on ideal $$I=\mathrm{id}<[x,x] \ | \ x\in L>$$ . [ABSTRACT FROM AUTHOR]

In the present article the classification of naturally graded 2-filiform Leibniz algebras is obtained. A splitting of the set of naturally graded Leibniz algebras into the families of Lie and non-Lie Leibniz algebras by means of characteristic sequences (isomorphism invariants) is proved. [ABSTRACT FROM AUTHOR]