This chapter addresses the basic theory of symplectic reduction by stages for central extensions. Examples are given in the following Chapter.
The main feature of this theory is that already after the first reduction, one encounters curvature, or magnetic terms and this complicates the subsequent reductions. To deal with this situation, we use the theory developed in the preceding chapter. The same sort of phenomenon also occurs in Lagrangian reduction by stages, as presented in Cendra, Marsden, and Ratiu [2001a].
Keywords
- Symplectic Form
- Central Extension
- Cotangent Bundle
- Coadjoint Orbit
- Stage Reduction
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Stages and Coadjoint Orbits of Central Extensions. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_8
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DOI: https://doi.org/10.1007/978-3-540-72470-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72469-8
Online ISBN: 978-3-540-72470-4
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