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
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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(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
Download citation
DOI: https://doi.org/10.1007/978-3-540-72470-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72469-8
Online ISBN: 978-3-540-72470-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
