Naturally graded Zinbiel algebras with nilindex n - 3

We present the classification of a subclass of n-dimensional naturally graded Zinbiel algebras. This subclass has the nilindex n − 3 and the characteristic sequence (n − 3, 2, 1). In fact, this result completes the classification of naturally graded Zinbiel algebras of nilindex n − 3

Leibniz Algebras Whose Semisimple Part is Related to sl2

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras sl1 2⊕sl2 2⊕· · ·⊕sls 2⊕R, where R is a solvable radical. The classifications of such Leibniz algebras in the cases dimR = 2, 3 and dimI 6= 3 have been obtained. Moreover, we classify Leibniz algebras with L/I ∼= sl1 2⊕sl2 2 and some conditions on ideal I = id < [x, x] | x ∈ L

Leibniz Algebras Constructed by Representations of General Diamond Lie Algebras

In this paper we construct a minimal faithful representation of the (2m + 2)- dimensional complex general Diamond Lie algebra, Dm(C), which is isomorphic to a subalgebra of the special linear Lie algebra sl(m + 2, C). We also construct a faithful representation of the general Diamond Lie algebra Dm which is isomorphic to a subalgebra of the special symplectic Lie algebra sp(2m + 2,R). Furthermore, we describe Leibniz algebras with corresponding (2m + 2)-dimensional general Diamond Lie algebra Dm and ideal generated by the squares of elements giving rise to a faithful representation of Dm.Ministerio de Economía y Competitividad MTM2013-43687-PXunta de Galicia GRC2013-04

One-generated nilpotent Novikov algebras

We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras.Ministerio de Economía y Competitividad MTM2016-79661-

Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra

In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un1, Un2 or Wn1 or Wn2.Ministerio de Economía y Competitividad MTM2013-43687-PXunta de Galicia GRC2013-04