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The existence of a coadjoint equivariant momentum mapping for a semidirect product


Author: Kentaro Mikami
Journal: Proc. Amer. Math. Soc. 82 (1981), 465-469
MSC: Primary 58F05; Secondary 70H99
DOI: https://doi.org/10.1090/S0002-9939-1981-0612741-X
MathSciNet review: 612741
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Abstract: We consider a symplectic action of a group $ G$ on a symplectic manifold $ P$, which admits a momentum mapping. Assume that $ G$ is a semidirect product of $ {G_1}$ by $ {G_2}$. We prove that if the symplectic action of $ {G_1}$ has a coadjoint equivariant momentum mapping, and if $ {H^1}(un{k_1}:{\mathbf{R}}) = {H^2}(un{k_2}:{\mathbf{R}}) = 0$, then the symplectic action of $ G$ has a coadjoint equivariant momentum mapping, where $ un{k_1}$ and $ un{k_2}$ are the Lie algebras of $ {G_1}$ and $ {G_2}$ respectively.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0612741-X
Keywords: Symplectic action, coajoint equivariant momentum mapping, semidirect product
Article copyright: © Copyright 1981 American Mathematical Society