Hyper-Lie Poisson structures

Ping Xu

Annales scientifiques de l'École Normale Supérieure (1997)

  • Volume: 30, Issue: 3, page 279-302
  • ISSN: 0012-9593

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Xu, Ping. "Hyper-Lie Poisson structures." Annales scientifiques de l'École Normale Supérieure 30.3 (1997): 279-302. <http://eudml.org/doc/82432>.

@article{Xu1997,
author = {Xu, Ping},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Kähler structures; symplectic geometry; Lie-Poisson structure},
language = {eng},
number = {3},
pages = {279-302},
publisher = {Elsevier},
title = {Hyper-Lie Poisson structures},
url = {http://eudml.org/doc/82432},
volume = {30},
year = {1997},
}

TY - JOUR
AU - Xu, Ping
TI - Hyper-Lie Poisson structures
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1997
PB - Elsevier
VL - 30
IS - 3
SP - 279
EP - 302
LA - eng
KW - Kähler structures; symplectic geometry; Lie-Poisson structure
UR - http://eudml.org/doc/82432
ER -

References

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  1. [1] M. F. ATIYAH, Hyper-Kähler manifolds (Collection : Complex Geometry and Analysis, Springer-Verlag Lecture Notes in Mathematics, Vol. 1422, 1990, pp. 1-13). Zbl0699.53068MR91g:53050
  2. [2] M. F. ATIYAH and N. J. HITCHIN, The geometry and dynamics of magnetic monopoles, Princeton University Press, 1988. Zbl0671.53001MR89k:53067
  3. [3] O. BIQUARD, Sur les équations de Nahm et la structure de Poisson des algèbres de Lie semi-simples complexes (Math. Ann. Vol. 304, 1996, pp. 253-276). Zbl0843.53027MR97c:53066
  4. [4] O. BIQUARD and P. GAUDUCHON, Hyperkähler metrics on cotangent bundles of hermitian symmetric spaces, preprint. Zbl0879.53051
  5. [5] S. K. DONALDSON, Nahm's equations and the classification of monopoles (Commun. Math. Phys. Vol. 96, 1984, pp. 387-407). Zbl0603.58042MR86c:58039
  6. [6] N. J. HITCHIN, Hyperkähler manifolds (Séminaire Bourbaki 44e année, No. 748, Astérisque, Vol. 206, 1992, pp. 137-166). Zbl0979.53051MR94f:53087
  7. [7] N. J. HITCHIN, A. KARLHEDE, U. LINSTROM and M. ROCEK, Hyperkähler metrics and supersymmetry, Commun. Math. Phys. Vol. 108, 1987, pp. 535-589. Zbl0612.53043
  8. [8] Y. KOSMANN-SCHWARZBACH and F. MAGRI, Poisson-Nijenhuis structures (Ann. Inst. H. Poincaré Phys. Théor. Vol. 53, 1990, pp. 35-81). Zbl0707.58048MR92b:17026
  9. [9] A. G. KOVALEV, Nahm's equations and complex adjoint orbits (Quart. J. Math. Oxford Ser. (2) Vol. 47, 1996, pp. 41-58). Zbl0852.53033MR97c:53070
  10. [10] P. B. KRONHEIMER, A hyper-Kählerian structure on coadjoint orbits of a semisimple complex group (J. of LMS, Vol. 42, 1990, pp. 193-208). Zbl0721.22006MR92b:53031
  11. [11] P. B. KRONHEIMER, Instantons and the geometry of the nilpotent variety (J. Diff. Geom. Vol. 32, 1990, pp. 473-490). Zbl0725.58007MR91m:58021
  12. [12] J. MARSDEN and A. WEINSTEIN, Reduction of symplectic manifolds with symmetry (Rep. Math. Phys. Vol. 5, 1974, pp. 121-129). Zbl0327.58005MR53 #6633
  13. [13] R. PENROSE, Nonlinear gravitons and curved twistor theory, Gen. Ralativ. Grav. Vol. 7, 1976, pp. 31-52. Zbl0354.53025MR55 #11905
  14. [14] M. VERGNE, Instantons et correspondance de Kostant-Sekiguchi, (C. R. Acad. Sci. Paris., t. 320, Série I, 1995, pp. 901-906). Zbl0833.22010MR96c:22026
  15. [15] A. WEINSTEIN, The local structure of Poisson manifolds, (J. Diff. Geom. Vol. 18, 1983, pp. 523-557). Zbl0524.58011MR86i:58059

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