Otto Ruttwig Campoamor Stursberg

Classification of (n−5)-filiform Lie algebras

Abstract In this paper we consider the problem of classifying the (n−5) -filiform Lie algebras. This is the first index for which infinite parametrized families appear, as can be seen in dimension 7. Moreover we obtain large families of characteristic nilpotent Lie algebras with nilpotence index 5 and show that at least for dimension 10 there is a characteristic nilpotent Lie algebra with nilpotence index 4 which is the algebra of derivations of a nilpotent Lie algebra.

An irreducible component of the variety of Leibniz algebras having trivial intersection with the variety of Lie algebras

We show the rigidity of a parameterized family of solvable Leibniz non-Lie algebras in arbitrary dimension, obtaining an irreducible component in the variety that does not intersect the variety of Lie algebras non-trivially. Moreover it is shown that for any the Abelian Lie algebra appears as the algebra of derivations of a solvable Leibniz algebra.We show the rigidity of a parameterized family of solvable Leibniz non-Lie algebras in arbitrary dimension, obtaining an irreducible component in the variety L epsilon(n) that does not intersect the variety of Lie algebras non-trivially. Moreover it is shown that for any n >= 3 the Abelian Lie algebra a(n) appears as the algebra of derivations of a solvable Leibniz algebra.