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

How to cite


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>.

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},

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 -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.