A filtration associated to an abelian inner ideal of a Lie algebra.

Abstract

Let B be an abelian inner ideal and let KerL B be the kernel of B. In this paper we show that when there exists n ∈ N with [B,KerL B] n ⊂ B, the inner ideal B induces a bounded filtration in L where B is the first nonzero submodule of the filtration and where the wings of the Lie algebra associated to the filtration coincide with the subquotient determined by B. This filtration extends the principal filtration induced by ad-nilpotent elements of index less than or equal to three defined in [E. García, M. Gómez Lozano, Principal filtrations of Lie algebras, Commun. Algebra 40 (10) (2012) 3622–3628].