Hi:

Given a finite dimensional Lie superalgebra G over field of complex number with decomposition G_{-1}+G_{0}+G_{1}, where G_{0} is the even part and G_{-1}+G_{1} is the odd part. Suppose F is the category of all finite dimensional weight G_{0}-modules. Is it a general fact that all irreducible(or indecomposable) highest weight module in F to be projective ? And, I'm not sure if the answer depends on the type of G.

Thank!!