On a class of finitary Lie algebras characterized through derivations

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 at least 2 such that dn 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.

(This paper has appeared in Proc. Amer. Math. Soc. 38 (12) (2010), 4161-4166.)


M. Bresar < matej.bresar@fmf.uni-lj.si >

A. Fernández López < emalfer@uma.es >