Groupoïdes symplectiques

A. Coste; P. Dazord; A. Weinstein

Publications du Département de mathématiques (Lyon) (1987)

  • Issue: 2A, page 1-62
  • ISSN: 0076-1656

How to cite

top

Coste, A., Dazord, P., and Weinstein, A.. "Groupoïdes symplectiques." Publications du Département de mathématiques (Lyon) (1987): 1-62. <http://eudml.org/doc/273582>.

@article{Coste1987,
author = {Coste, A., Dazord, P., Weinstein, A.},
journal = {Publications du Département de mathématiques (Lyon)},
keywords = {symplectic manifold; Lie groupoid; Lie algebroid; symplectic groupoids and algebroids; symplectic mechanics},
language = {fre},
number = {2A},
pages = {1-62},
publisher = {Université Claude Bernard - Lyon 1},
title = {Groupoïdes symplectiques},
url = {http://eudml.org/doc/273582},
year = {1987},
}

TY - JOUR
AU - Coste, A.
AU - Dazord, P.
AU - Weinstein, A.
TI - Groupoïdes symplectiques
JO - Publications du Département de mathématiques (Lyon)
PY - 1987
PB - Université Claude Bernard - Lyon 1
IS - 2A
SP - 1
EP - 62
LA - fre
KW - symplectic manifold; Lie groupoid; Lie algebroid; symplectic groupoids and algebroids; symplectic mechanics
UR - http://eudml.org/doc/273582
ER -

References

top
  1. [A, M. 1978] R. Abraham et J.E. Marsden, Foundations of Mechanics, Benjamin Ed. 1978. Zbl0393.70001MR515141
  2. [A1. MO 1985] R. Almeida et P. Molino, Suites d'Atiyah et feuilletages trans-versalement complets. C.R. Acad. Sc.Paris Ser. I (300) 13-15. Zbl0582.57015MR778785
  3. [B.F.F.L.S. 1978] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternhaimer, Deformation theory and quantization, Ann. Phys.111 (1978), 61-151. Zbl0377.53025
  4. [C. 1982] A. Connes, A survey of foliations and operator algebras, in operator Algebras and Applications (Kadison ed.) Proc. Symp. Pure Math., Vol. 38, Amer. Math. Soc.Providence, R.I. (1982), 521-628. Zbl0531.57023MR679730
  5. [D. 1985] P. Dazord, Feuilletages à singularités, Indag. Math. Volumen 47 (1) (1985) 21-39. Zbl0584.57016MR783003
  6. [DO. LA. 1966] A. Douady et M. Lazard, Espaces fibrés en algèbres de Lie et en groupes, Invent. Math.1 (1966), 133-151. Zbl0144.01804MR197622
  7. [Dr. 1983] V.G. Drinfel'd, Hamiltonian structures on Lie groups, Lie bi- algebras and the geometrical meaning of the classical Yang-Baxter equations. Soviet Math. Dokl Vol. 27 (1983) n° 1. Zbl0526.58017MR688240
  8. [Du. He. 1982] J.J. Duistermaat and H. J. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math.69 (1982), 259-268. Zbl0503.58015MR674406
  9. [E.] C. Ehresmann, Œuvres complètes. 
  10. [V.E. 1984)] W.T. van Est, Rapport sur les S-atlas, Structure transverse des feuilletages, Astérisque116 (1984) 235-292. Zbl0543.58003MR755174
  11. [V.E. 1987] W.T. van Est, Une démonstration de E. Cartan du 3ème théorème de Lie. A paraître dans "Actions hamiltoniennes de groupes. Troisième théorème de Lie ". Travaux en Cours. Hermann Editeur. Zbl0652.17002
  12. [V.E.K. 1964] W.T. van Est et T.J. Kortkagen, Non enlargible Lie algebra, Indag. Math.26 (1964), 15-31. Zbl0121.27503MR160851
  13. [V.E. VL. 1987] W.T. van Est et M. van der Lee, On the enlargibility criteria for local groups due to Malov and Cartan. A paraître dans "Actions hamiltoniennes de groupes. Troisième théorème de Lie". Coll. Travaux en Cours. Hermann Editeur. 
  14. [G. 1958] R. Godement, Théorie des faisceaux, Actualités Scientifiques et Industrielles, 1252. Hermann Ed. Paris. Zbl0080.16201MR102797
  15. [H. 1984] A. Haefliger, Groupoïdes d'holonomie et classifiants, Structure transverse des Feuilletages, Astérisque116 (1984), 70-97. Zbl0562.57012MR755163
  16. [K. 1985] M.V. Karasev, Quantization of non linear Lie-Poisson brackets in quasi-classical approximation, Preprint ITF Akad. Nauk SSR, ITF - 85 - 72R, KIEV (1985). 
  17. [K. 1986] M.V. Karasev, Poisson symmetry algebras and the asymptotics of spectral series, Functional Anal. Appl.20 (1986), 17-26. Zbl0629.58017MR831045
  18. [K. M. 1981] M.V. Karasev and V.P. Maslov, Operators with general commutation relations and their applications I, Unitary- non linear operator equations, J. Soviet Math.15 (1981), 273-368. Zbl0482.58029
  19. [K. M. 1984] M.V. Karasev and V.P. Maslov, Asymptotic and geometric quantization Russian Math.Surveys39 - 6 (1984), 133-205. Zbl0588.58031MR771100
  20. [Ki. 1976] A.A. Kirillov, Local Lie algebra. Russ. Math. Surveys (31) 55-751976. Zbl0357.58003MR438390
  21. [Lib. 1972] P. Libermann, Sur les groupoïdes différentiables et le "presque parallélisme", Symposia Math.10 (1972), 59-93. Zbl0265.53030MR370668
  22. [Lib. 1983] P. Libermann, Problèmes d'équivalence et géométrie symplectique, Astérisque107-108 (1983), 43-69. Zbl0529.53030
  23. [Lic. 1955] A. Lichnerowicz, Théorie globale des connexions et des groupes d'holonomie, Ed. Cremonese Rome1955. Zbl0116.39102
  24. [Lic. 1977] A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geom.12, (1977), 253-300. Zbl0405.53024MR501133
  25. [Lic. 1982] A. Lichnerowicz, Variétés de Poisson et feuilletages. Ann. Fac.Sc.Toulouse, Vol. IV1982. 195-262. Zbl0517.58029MR701731
  26. [M. W.] K. Mikami and A. Weinstein, en préparation. 
  27. [Pl. 1980] M. Plaisant, Q-variétés banachiques. Application à l'intégrabilité des algèbres de Lie, C.R. Acad. Sc.Paris290 A (1980),185-188. Zbl0431.58007MR564157
  28. [Pr. 1966] J. Pradines, C.R. Acad. Sc.Paris263 (1966), 907-910. Zbl0147.41102MR214103
  29. [Pr. 1967] J. Pradines, Théorie de Lie par les groupoïdes différentiables, C.R. Acad. Sc.Paris264A (1967), 245-248. Zbl0154.21704MR216409
  30. [Pr. 1968] J. Pradines, Troisième théorème de Lie sur les groupoïdes différentiablesC.R. Acad. Sc.Paris267 (1968), 21-23. Zbl0172.03502MR231414
  31. [Pr. 1984] J. Pradines, Holonomie et grapes locaux, C.R. Acad. Sc.Paris298 A (1984), 297-300. Zbl0568.57018MR765427
  32. [Pr. 1985] J. Pradines, 
  33. [R. 1980] J. Renault,A groupoïd approach to C*-algebras, Lecture Notes in Math., Vol. 793, Springer-Verlag1980. Zbl0433.46049MR584266
  34. [S. 1977] Sternberg, On minimal coupling and the symplecti mechanics of a classical particle in the presence of a Yang-Mills field. Proc. Nat. Acad. Sc.74 (1977) - 5253-5254. Zbl0765.58010MR458486
  35. [S.T.S. 1983] M.A. Semenov-Tyan-Shanskii, What is a classical R-matrix ? Functional Anal. Appl.17 (1983), 259-272. Zbl0535.58031
  36. [St. 1974] P. Stefan, Accessibility and foliations with singularities, Bull. Amer. Math. Soc., 80 (1974), 1142-1145. Zbl0293.57015MR353362
  37. [Su. 1973] H.J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. of Amer. Math. Soc., 180 (1973), 171-188. Zbl0274.58002
  38. [W. 1978] A. Weinstein, A universal phase space for particles in Yan-Mills fields, Lett. Math. Phys.2 (1978), 417-420. Zbl0274.58002MR321133
  39. [W. 1979] A. Weinstein, Lectures on symplectic manifolds Regional Conferences series in Math. n° 29, Amer. Math. Soc Zbl0388.58010MR507025
  40. [W. 1981] A. Weinstein, Symplectic geometry, Bull. Amer. Math. Soc.5 (1981) 1-13. Zbl0406.53031MR598470
  41. [W. 1983] A. Weinstein, The local Structure of Poisson manifolds, J. Diff. Geom.18 (1983), 523-557. Zbl0465.58013MR614310
  42. [W. 1987] A. Weinstein, Symplectic groupoïds and Poisson manifolds, Bull. Amer. Math. Soc16 (1987), 101-103. Zbl0524.58011MR723816
  43. [W. 1987 b] A. Weinstein, Poisson geometry of the principal series and non linearizable structure, preprint. Zbl0618.58020MR866024

Citations in EuDML Documents

top
  1. Charles-Michel Marle, On submanifolds and quotients of Poisson and Jacobi manifolds
  2. Ping Xu, Morita equivalence and symplectic realizations of Poisson manifolds
  3. Henrique Bursztyn, Olga Radko, Gauge equivalence of Dirac structures and symplectic groupoids
  4. P. Dazord, D. Sondaz, Chapitre I Variétés de Poisson - Algébroïdes de Lie
  5. C. Albert, P. Dazord, Théorie des groupoïdes symplectiques
  6. P.M. Kouotchop Wamba, A. MBA, The infinitesimal counterpart of tangent presymplectic groupoids of higher order
  7. C. Albert, P. Dazord, Théorie des groupoïdes symplectiques
  8. Ping Xu, Poisson cohomology of regular Poisson manifolds
  9. Jan Kubarski, The Chern-Weil Homomorphism of Regular Lie Algebroids
  10. Jan Kubarski, Connections in regular Poisson manifolds over ℝ-Lie foliations

NotesEmbed ?

top

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.