Marsden, J. E., G. Misiolek, M. Perlmutter and T. S. Ratiu
We shall start with the classical cases of commuting reduction (first appearing in Marsden and Weinstein [1974]) and present a new proof and approach to semidirect product theory. We shall then give an idea of how the more general theory of group extensions proceeds (the details of which are given in Marsden, Misioek, Perlmutter and Ratiu [1998]). The case of central extensions is illustrated in this paper with the example of the Heisenberg group. The theory, however, applies to many other interesting examples such as the Bott-Virasoro group and the KdV equation.