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Stages and Semidirect Products with Cocycles

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

This chapter is concerned with two major themes. The first theme, which is presented in §10.1 and §10.2, deals with the semidirect product M of a group G with an Abelian group A, where the construction of the semidirect product itself involves an A-valued cocycle of G. In this context, A (which is N in the general theory) is still a normal subgroup and the reduction by stages program is fully carried out. In particular, the stages hypothesis holds and so the reduction by stages program for the action of M on a symplectic manifold can be implemented.We focus on the case of the action of M on T*M (by the lift of right translation) so that the final reduced spaces will be the coadjoint orbits of M.

Keywords

  • Symplectic Manifold
  • Poisson Structure
  • Semidirect Product
  • Cotangent Bundle
  • Isotropy Subgroup

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). Stages and Semidirect Products with Cocycles. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_10

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