Homomorphisms of the Lie algebras associated with a symplectic manifold

C. J. Atkin; J. Grabowski

Compositio Mathematica (1990)

  • Volume: 76, Issue: 3, page 315-349
  • ISSN: 0010-437X

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Atkin, C. J., and Grabowski, J.. "Homomorphisms of the Lie algebras associated with a symplectic manifold." Compositio Mathematica 76.3 (1990): 315-349. <http://eudml.org/doc/90060>.

@article{Atkin1990,
author = {Atkin, C. J., Grabowski, J.},
journal = {Compositio Mathematica},
keywords = {symplectic manifold; Lie algebras; Poisson brackets; Hamiltonian vector fields},
language = {eng},
number = {3},
pages = {315-349},
publisher = {Kluwer Academic Publishers},
title = {Homomorphisms of the Lie algebras associated with a symplectic manifold},
url = {http://eudml.org/doc/90060},
volume = {76},
year = {1990},
}

TY - JOUR
AU - Atkin, C. J.
AU - Grabowski, J.
TI - Homomorphisms of the Lie algebras associated with a symplectic manifold
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 76
IS - 3
SP - 315
EP - 349
LA - eng
KW - symplectic manifold; Lie algebras; Poisson brackets; Hamiltonian vector fields
UR - http://eudml.org/doc/90060
ER -

References

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  1. 1 C.J. Atkin, A note on the algebra of Poisson brackets, Math. Proc. Camb. Phil. Soc.96 (1984), 45-60. Zbl0543.17010MR743700
  2. 2 A. Avez, A. Diaz-Miranda and A. Lichnerowicz, Sur l'algèbre des automorphismes infinitésimaux d'une variété symplectique, J. Diff. Geom.9 (1974), 1-40. Zbl0283.53033MR356131
  3. 3 G.E. Bredon, Sheaf Theory; McGraw-Hill, New York, 1967. Zbl0158.20505MR221500
  4. 4 Séminaire Cartan (École Normale Supérieure), 1951/52. 
  5. 5 R. Godement, Topologie Algébrique et Théorie des Faisceaux; Hermann, Paris, 1958. Zbl0080.16201MR102797
  6. 6 J. Grabowski, Isomorphisms and ideals of the Lie algebras of vector fields, Invent., Math.50 (1978), 13-33. Zbl0378.57010MR516602
  7. 7 J. Grabowski, The Lie structure of C* and Poisson algebras, Studia Math.81 (1985), 259-270. Zbl0536.46043MR808568
  8. 8 H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. Math.68 (1958), 460-472. Zbl0108.07804MR98847
  9. 9 B. Kaup and L. Kaup, Holomorphic Functions in Several Variables, de Gruyter, Berlin-New York1983. Zbl0528.32001
  10. 10 A. Lichnerowicz, Sur les variétés symplectiques, C.R. Acad. Sci. Paris233 (1951), 723-726. Zbl0044.18602MR46732
  11. 11 D McDuff, Symplectic diffeomorphisms and the flux homomorphism, Invent. Math.77 (1984), 353-366. Zbl0538.53041MR752824
  12. 12 R. Narasimhan, Imbedding of holomorphically complete complex spaces, Amer. J. Math.82 (1960), 917-934. Zbl0104.05402MR148942
  13. 13 A. Tognoli, Some results in the theory of real analytic spaces, Espaces Analytiques (Séminaire, Bucharest, 1969), 149-157; Editura Acad. R.S.R., Bucharest, 1971. Zbl0219.32005MR284612
  14. 14 H. Whitney, Differentiable manifolds, Ann. Math.37 (1936), 645-680. Zbl0015.32001MR1503303JFM62.1454.01

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