On a class of finitary Lie algebras characterized through derivations

Abstract

Abstract. Let L be an infinite-dimensional simple Lie algebra over a field of characteristic 0. Then there exist a derivation d on L and n ≥ 2 such that d n is a nonzero finite rank map if and only if L is finitary and contains a nonzero finite-dimensional abelian inner ideal. This is a partial statement of our main theorem. As auxiliary results needed for the proof we establish some properties of derivations in general nonassociative algebras.