Poisson structures and Lie algebras
Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 421-434. 
@incollection{AST_1985__S131__421_0,
     author = {Weinstein, Alan},
     title = {Poisson structures and {Lie} algebras},
     booktitle = {\'Elie Cartan et les math\'ematiques d'aujourd'hui - Lyon, 25-29 juin 1984},
     series = {Ast\'erisque},
     pages = {421--434},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {S131},
     year = {1985},
     mrnumber = {837210},
     zbl = {0608.58027},
     language = {en},
     url = {http://www.numdam.org/item/AST_1985__S131__421_0/}
}
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Weinstein, Alan. Poisson structures and Lie algebras, dans Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 421-434. http://www.numdam.org/item/AST_1985__S131__421_0/

[A1] Arnol'D (V. I.). - An a priori estimate in the theory of hydrodynamic stability, Amer. Math. Soc. Transl., t. 19, 1969, p. 267-269. | Zbl

[A2] Arnol'D (V. I.). - Remarks on the stationary phase method and Coxeter numbers, Russian Math. Surveys, t. 28, n°5, 1973, p. 19-48. | DOI | MR | Zbl

[A3] Arnol'D (V. I.). - Mathematical methods of classical mechanics. - New York, Springer, 1978 (Graduate Texts in Math., 60). | DOI | MR | Zbl

[BE] Berezin (F. A.). - Some remarks about the associated envelope of a Lie algebra, Funct. Anal. Appl, t. 1, 1967, p. 91-102. | DOI | MR | Zbl

[BO] Bourbaki (N.). - Groupes et algèbres de Lie, Ch. 7 et 8. - Paris, Hermann, 1975. | Zbl

[CA1] Cartan (É.). - Sur les petites oscillations d'une masse fluide, Bull. Sc. Math., t. 46, 1922, p. 317-352 et 356-369. | JFM

[CA2] Cartan (É.). - Sur la stabilité ordinaire des ellipsoides de Jacobi, Proc. Int. Math. Cong. Toronto, t. 2, p. 9-17. | JFM

[CO1] Conn (J.). - Normal forms for analytic Poisson structures, Annals of Math., t. 119, 1984, p. 577-601. | DOI | MR | Zbl

[CO2] Conn (J.) - Normal forms for smooth Poisson structures, Annals of Math., (to appear). | MR | Zbl

[DA] Dazord (P.). - Stabilité et linéarisation dans les variétés de Poisson, Séminaire Sud-Rhodanien de géométrie, Mai 1984, (to appear). | Zbl

[DU] Duflo (M.). - Private communication.

[DU-V] Duflo (M.) and Vergne (M.). - Une propriété de la représentation coadjointe d'une algèbre de Lie, C.R. Acad. Sci. Paris, Sér. A-B, t. 268, 1969, p. A583-A585. | MR | Zbl

[F-W] Fortune (B.) and Weinstein (A.). - A symplectic fixed point theorem for complex projective spaces, Bull. Amer. Math. Soc., t. 12, 1985, p. 128-130. | DOI | MR | Zbl

[G-DI] Gelfand (I. M.) and Dikii (L. A.). - Families of hamiltonian structures connected with integrable nonlinear differential equations, preprint n° 136, Inst. Appl. Math. USSR Acad. Sci., 1978, (in Russian). | MR

[G-DO1] Gelfand (I. M.) and Dorfman (I. Ya.). - Hamiltonian operators and algebraic structures related to them, Funct. Anal. Appl., t. 13, 1979, p. 248-262. | DOI | MR | Zbl

[G-DO2] Gelfand (I. M.) and Dorfman (I. Ya.). - Hamiltonian operators and infinite-dimensional Lie algebras, Funct. Anal. Appl., t. 15, 1981, p. 173-187. | DOI | MR | Zbl

[GI] Givental (A. B.). - Private communication via V.I. Arnol'd.

[GO] Gotay (M. J.). - Poisson reduction and quantization for the n+1 photon, J. Math. Phys., t. 25, 1984, p. 2154-2159. | DOI | MR | Zbl

[M-R-W] Holm (D.), Marsden (J.), Ratiu (T.), and Weinstein (A.). - Nonlinear stability of fluid and plasma systems, Physics Reports (to appear). | MR | Zbl

[HO] Howe (R.). - Remarks on classical invariant theory (unpublished manuscript). | Zbl

[K-K-S] Kazhdan (D.), Kostant (B.), and Sternberg (S.). - Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math., t. 31, 1978, p. 481-508. | DOI | MR | Zbl

[KO] Kostant (B.). - Private communication.

[L] Lie (S.). - Theorie der Transformationsgruppen. - Leipzig, Teubner (Zweiter Abschnitt, unter Mitwirkung von Prof. Dr. Friedrich Engel) 1890. | JFM

[M] Magri (F.). - A simple model of the integrable Hamiltonian equation, J. Math. Phys, t. 19, 1978, p. 1156-1162. | DOI | MR | Zbl

[MA] Marsden (J.), ed.- Fluids and plasmas : Geometry and dynamics [Proc. A.M.S. Conference, Boulder. 1983]. - Providence, R.I., Amer. Math. Soc., 1984 (Contemp. Math., 28). | MR | Zbl

[MA-R-W] Marsden (J.), Ratiu (T.), and Weinstein (A.). - Semidirect products and reduction in mechanics, Trans. Amer. Math. Soc., t. 281, 1984, p. 147-177. | DOI | MR | Zbl

[MA-W1] Marsden (J.) and Weinstein (A.). - The hamiltonian structure of the Maxwell-Vlasov equations, Physica, t. 4 D, 1982, p. 394-406. | MR | Zbl

[MA-W2] Marsden (J.) and Weinstein (A.). - Coadjoint orbits, vertices, and Clebsch variables for incompressible fluids, Physica, t. 7 D, 1983, p. 305-323. | MR | Zbl

[ME] Medina (A.). - Structure orthogonale sur une algèbre de Lie et structure de Lie-Poisson associée, Séminaire de géométrie différentielle, 1983-1984, Montpellier, p. 113-121. | Zbl

[MI-F] Mishchenko (A. S.) and Fomenko (A. T.). - Euler equations on finite dimensional Lie groups, Math. USSR Izvestia, t. 12, 1978, p. 371-389. | DOI | MR | Zbl

[MO] Molino (P.). - Structure transverse aux orbites de la représentation coadjointe : le cas des orbites réductives, Séminaire de Géométrie différentielle, 1983-1984, Montpellier, p. 55-62. | Zbl

[R] Ratiu (T.). - Involution theorems, Geometric Methods in Mathematical Physics [G. Kaiser and J.E. Marsden, eds., Proc. NSF-CBMS conf., Univ. of Lowell, Mass., March 19-23, 1979], p. 219-257 . - Berlin, Springer-Verlag 1980, (Lecture Notes in Math., 775). | DOI | MR | Zbl

[SN-W] Sniatycki (J.) and Weinstein (A.). - Reduction and quantization for singular momentum mappings, Lett. Math. Phys., t. 7, 1983, p. 159-161. | MR | Zbl

[SO] Souriau (J. M.). - Structure des systèmes dynamiques. - Paris, Dunod, 1970. | MR | Zbl

[T-F] Trofimov (V. V.) and Fomenko (A. T.). - Liouville integrability of hamiltonian systems on Lie algebras, Uspekhi Mat. Nauk, t. 39, n° 2, 1984, p. 3-56 (in Russian). | MR | Zbl

[W1] Weinstein (A.). - The local structure of Poisson manifolds, J. Diff. Geom, t. 18, 1983, p. 523-557. | DOI | MR | Zbl

[W2] Weinstein (A.). - Stability of Poisson-Hamilton equilibria, Fluids and plasmas : Geometry and dynamics [Proc. A.M.S. conference, Boulder. 1983], p. 3-13. - Providence, R.I., Amer. Math. Soc., 1984 (Contemp. Math., 28). | MR | Zbl