${\mathfrak{g}}_0$-Geometry and Its Relationship with Stable Representations

This paper explores the sheaves with the action of a lie algebra and computes their cohomology in a new category. Then in the following sections, We try to generalize a classical result in [GM, Ch. IV] about exterior algebra. We add the action of ${\mathfrak{g}}_0$ and prove that there is still a faithful functor.