Hi:

Given a finite dimensional Lie superalgebra $G$ over the field of complex numbers 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 modules in $F$ are projective ? And, I'm not sure if the answer depends on the type of $G$.

Thanks!!