Representations of finitary Lie algebras

Let F be an algebraically closed field of characteristic ≠2,3, W a F-vector space and with nilWL=(0), dimFL=∞. Suppose is a finitary subalgebra. The faithful irreducible L-modules are determined. It is shown that L has minimal ideals. If a minimal ideal S is infinite-dimensional then SW is a completely reducible L-module. Suppose , W is L-irreducible and char(F)>3. Then L is classified in terms of .