The BGG Representation Category For Generalised Reductive Lie Algebras

This paper extends the BGG category over complex semi-simple Lie algebra to the category over generalised reductive Lie algebras.In the article,we make a preliminary study of the highest weight modules and the projective modules in this new category,and generate some conclusions in the classical case.And we prove that a projective module of semisimple Lie algebras may not be a projective module of generalised reductive Lie algebras,but a new object is constructed to make the similar BGG Reciprocity valid.