  We introduce a notion of scalar curvature of a twisted generalized Kahler
manifold in terms of pure spinors formalism. A moment map framework with a
modified action of generalized Hamiltonians on an arbitrary compact generalized
Kahler manifold is developed. Then it turns out that a moment map is given by
the scalar curvature, which is a generalization of the result of the scalar
curvature as a moment map in the ordinary Kahler geometry, due to Fujiki and
Donaldson.
  A noncommutative compact Lie group $G$ does not have any Kahler structure.
However, we show that every compact Lie group admits generalized Kahler
structures with constant scalar curvature. In particular, generalized Kahler
structures with constant scalar curvature on the standard Hopf surface are
explicitly given.
