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 on a symplectic manifold , which admits a momentum mapping. Assume that is a semidirect product of by . We prove that if the symplectic action of has a coadjoint equivariant momentum mapping, and if , then the symplectic action of has a coadjoint equivariant momentum mapping, where and are the Lie algebras of and respectively.

**[1]**Ralph Abraham and Jerrold E. Marsden,*Foundations of mechanics*, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR**515141****[2]**G.-M. Marle,*Symplectic manifolds, dynamical groups, and Hamiltonian mechanics*, Differential geometry and relativity, Reidel, Dordrecht, 1976, pp. 249–269. Mathematical Phys. and Appl. Math., Vol. 3. MR**0438393****[3]**J.-M. Souriau,*Structure des systèmes dynamiques*, Maîtrises de mathématiques, Dunod, Paris, 1970 (French). MR**0260238****[4]**Nolan R. Wallach,*Symplectic geometry and Fourier analysis*, Math Sci Press, Brookline, Mass., 1977. With an appendix on quantum mechanics by Robert Hermann; Lie Groups: History, Frontiers and Applications, Vol. V. MR**0488148****[5]**Alan Weinstein,*Lectures on symplectic manifolds*, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976; Regional Conference Series in Mathematics, No. 29. MR**0464312**

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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