## Projective objects in BGG category O\mathcal{O} are projective U(g)U(\mathfrak{g})-modules?

Let g be a finite dimensional semi-simple complex Lie algebra. Then, BGG category O is defined to be the full subcategory of finitely generated U(g)-modules of those modules which are weight modules and locally U(n)-finite. It is known that O is not extension-closed in the category of (finitely generated) U(g)-modules, see e.g. this math.stackexchange question. … Read more