  Starting from vector fields that preserve a differential form on a Riemann
sphere with Grassmann variables, one can construct a Superconformal Algebra by
considering central extensions of the algebra of vector fields. In this note,
the N=4 case is analyzed closely, where the presence of weight zero operators
in the field theory forces the introduction of non-central extensions. How this
modifies the existing Field Theory, Representation Theory and Gelfand-Fuchs
constructions is discussed. It is also discussed how graded Riemann sphere
geometry can be used to give a geometrical description of the central charge in
the N=1 theory.
