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Optimal Reduction by Stages

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

As we already saw in Part II, the reduction by stages procedure consists of carrying out reduction in two shots using the normal subgroups of the symmetry group. To be more specific, suppose that we are in the same setup as Theorem 13.5.1 and that the symmetry group G has a closed normal subgroup N. In this chapter we will spell out the conditions under which optimal reduction by G renders the same result as reduction in the following two stages: we first reduce by N; the resulting space inherits symmetry properties coming from the quotient Lie group G/N that can be used to reduce one more time.

Keywords

  • Normal Subgroup
  • Symplectic Manifold
  • Isotropy Subgroup
  • Polar Distribution
  • Poisson Manifold

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2007 Springer-Verlag Berlin Heidelberg

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(2007). Optimal Reduction by Stages. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_15

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