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Group Extensions and the Stages Hypothesis

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1913)

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.

Keywords

  • Poisson Bracket
  • Central Extension
  • Semidirect Product
  • Jacobi Identity
  • Group Extension

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© 2007 Springer-Verlag Berlin Heidelberg

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(2007). Group Extensions and the Stages Hypothesis. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_6

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