A convexity theorem for Poisson actions of compact Lie groups

Hermann Flaschka; Tudor Ratiu

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 6, page 787-809
  • ISSN: 0012-9593

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Flaschka, Hermann, and Ratiu, Tudor. "A convexity theorem for Poisson actions of compact Lie groups." Annales scientifiques de l'École Normale Supérieure 29.6 (1996): 787-809. <http://eudml.org/doc/82423>.

@article{Flaschka1996,
author = {Flaschka, Hermann, Ratiu, Tudor},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Poisson Lie group; momentum mapping; convexity},
language = {eng},
number = {6},
pages = {787-809},
publisher = {Elsevier},
title = {A convexity theorem for Poisson actions of compact Lie groups},
url = {http://eudml.org/doc/82423},
volume = {29},
year = {1996},
}

TY - JOUR
AU - Flaschka, Hermann
AU - Ratiu, Tudor
TI - A convexity theorem for Poisson actions of compact Lie groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 6
SP - 787
EP - 809
LA - eng
KW - Poisson Lie group; momentum mapping; convexity
UR - http://eudml.org/doc/82423
ER -

References

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  2. [A] M. F. ATIYAH, Convexity and commuting Hamiltonians (Bull. London Math. Soc., Vol. 14, 1982, pp. 1-15). Zbl0482.58013MR83e:53037
  3. [Br] G. E. BREDON, Introduction to Compact Transformation Groups, Academic Press, New York and London, 1972. Zbl0246.57017MR54 #1265
  4. [CK] S. CHEMLA and Y. KARSHON, Convexity of the moment map for nonabelian compact groups ; a proof by M. CONDEVAUX, P. DAZORD and P. MOLINO (Unpublished lecture notes, MIT, February 1991). 
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  9. [HNP] J. HILGERT, K.-H. NEEB and W. PLANK, Symplectic convexity theorems and coadjoint orbits (Comp. Math., Vol. 94, 1994, pp. 129-180). Zbl0819.22006MR96d:53053
  10. [J] K. JÄNICH, Differenzierbare G-Mannigfaltigkeiten (Lecture Notes in Math., Vol. 59, 1968, Springer-Verlag). Zbl0159.53701MR37 #4835
  11. [Ka] T. KATO, Perturbation Theory for Linear Operators (Die Grundlehren der Mathematischen Wissenschaften, Vol. 132, Springer Verlag, New York-Berlin-Heidelberg, 1966). Zbl0148.12601MR34 #3324
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  13. [LS] S. LEVENDORSKIĬ and Y. SOIBELMAN, Algebras of functions on compact quantum groups, Schubert cells and quantum tori (Comm. Math. Phys. Vol. 139, 1991, pp. 141-170). Zbl0729.17011MR92h:58020
  14. [Lu1] J.-H. LU, Multiplicative and Affine Poisson Structures on Lie Groups, (Ph. D. dissertation, University of California at Berkeley, 1990). 
  15. [Lu2] J.-H. LU, Momentum mappings and reduction of Poisson actions, in Proc. of the Sém. Sud-Rhodanien de Géométrie at Berkeley, 1989, Springer Verlag MSRI Series, 1991. 
  16. [LuRa] J.-H. LU and T. RATIU, On the nonlinear convexity theorem of Kostant (J. A.M.S., Vol. 4, 1991, pp. 349-363). Zbl0785.22019MR92a:58048
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