Group Extensions and the Stages Hypothesis

As was discussed in the general setting of reduction by stages, we consider a Lie group M with a normal subgroup N; recall that the goal is to reduce the action ofM in two stages, the first stage being reduction by N. The goal of this chapter is to introduce hypotheses under which reduction by stages works—that is, the stages hypothesis (see Definition 5.2.8) is automatically satisfied. The actual reduction by stages procedure for these examples will be carried out in Chapters 8, 9, and 10.