Cohomology of Pseudounitary Unimodular Lie Groups

In this thesis we examine the properties of the family of Lie groups SU_p,q and its associated Lie algebra su_p,q. In particular we investigate certain decompositions of these objects and use these decompositions to create quotient spaces of both the group structure and the algebra structure. We then introduce cohomology in an algebraic manner and prove a result that relates the zeroth cohomology group of the tangent bundles of certain quotient spaces to the complexification of su_p,q. We then examine a way to generalize the decompositions of the quotient groups of SU_p,q even further.