Local Lie algebra structure and momentum mapping

Kentaro MIKAMI

doi:10.2969/jmsj/03920233

Kentaro MIKAMI

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 2 Pages 233-246

DOI https://doi.org/10.2969/jmsj/03920233

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Published: 1987 Received: August 28, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) Y. Hatakeyama, Some notes on the group of automorphisms of contact and symplectic structures, Tohoku Math. J., 18 (1966), 338-347.
2) A. A. Kirillov, Local Lie algebras, Russian Math. Surveys, 31-4 (1976), 55-75 (from Uspekhi Mat. Nauk., 31-4 (1976), 57-76).
3) C.-M. Marle, Lie group actions on a canonical manifold, Symplectic Geometry (Toulouse, 1981), Res. Notes in Math., 80, Pitman, Boston-London, 1983, pp. 144-166.
4) K. Mikami, The existence of a coadjoint equivariant momentum mapping for a semidirect product, Proc. Amer. Math. Soc., 82 (1981), 465-469.
5) R. Ouzilou, Hamiltonian actions on Poisson manifolds, Symplectic Geometry (Toulouse, 1981), Res. Notes in Math., 80, Pitman, Boston-London, 1983, pp. 172-183.
6) J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970.
7) W. M. Tulczyjew, Poisson brackets and canonical manifolds, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 22 (1974), 931-935.
8) W. M. Tulczyjew, The graded Lie algebra of multivector fields and the generalized Lie derivative of forms, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 22 (1974), 937-942.
9) A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conf. Ser. in Math., 29, Amer. Math. Soc., Providence, 1977.
10) A. Weinstein, The local structure of Poisson manifolds, J. Differential Geometry, 18 (1983), 523-557.

Right : [1] Y. Hatakeyama, Some notes on the group of automorphisms of contact and symplectic structures, Tôhoku Math. J., 18 (1966), 338-347.
[2] A. A. Kirillov, Local Lie algebras, Russian Math. Surveys, 31-4 (1976), 55-75 (from Uspekhi Mat. Nauk., 31-4 (1976), 57-76).
[3] C.-M. Marle, Lie group actions on a canonical manifold, Symplectic Geometry (Toulouse, 1981), Res. Notes in Math., 80, Pitman, Boston-London, 1983, pp. 144-166.
[4] K. Mikami, The existence of a coadjoint equivariant momentum mapping for a semidirect product, Proc. Amer. Math. Soc., 82 (1981), 465-469.
[5] R. Ouzilou, Hamiltonian actions on Poisson manifolds, Symplectic Geometry (Toulouse, 1981), Res. Notes in Math., 80, Pitman, Boston-London, 1983, pp. 172-183.
[6] J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970.
[7] W. M. Tulczyjew, Poisson brackets and canonical manifolds, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 22 (1974), 931-935.
[8] W. M. Tulczyjew, The graded Lie algebra of multivector fields and the generalized Lie derivative of forms, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 22 (1974), 937-942.
[9] A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conf. Ser. in Math., 29, Amer. Math. Soc., Providence, 1977.
[10] A. Weinstein, The local structure of Poisson manifolds, J. Differential Geometry, 18 (1983), 523-557.

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