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!!

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!!