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

Abstract

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.