Moments and reduction for symplectic groupoids
Kentaro Mikami and Alan Weinstein
Source: Publ. Res. Inst. Math. Sci. Volume 24, Number 1 (1988), 121-140.
Primary Subjects: 58F05
Secondary Subjects: 20L15, 53C57
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.prims/1195175328
Mathematical Reviews number (MathSciNet):
MR944869
Zentralblatt MATH identifier:
0659.58016
Digital Object Identifier: doi:10.2977/prims/1195175328
References
[1] Abraham, R. and Marsden, J. E., Foundations of mechanics, 2nd ed. New York: Benjamin/Cummings, 1978.
Mathematical Reviews (MathSciNet):
MR515141
Zentralblatt MATH:
0393.70001
[2] Brown, R., Danesh-Naruie, G. and Hardy, J. P. L., Topological groupoids: II. Covering morphisms and G-spaces, Math. Nachr., 74 (1976), 143-156.
Mathematical Reviews (MathSciNet):
MR442937
Zentralblatt MATH:
0281.22002
[3] Coste, A., Dazord, P. and Weinstein, A., Groupoides symplectiques. Publications du Department de Mathematiques de l'University de Lyon I, 2/A (1987).
Mathematical Reviews (MathSciNet):
MR996653
Zentralblatt MATH:
0668.58017
[4] Drinfel'd, V. G., Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations, Soviet Math. Dokl. 9 27(1983), 68-71.
Mathematical Reviews (MathSciNet):
MR688240
Zentralblatt MATH:
0526.58017
[5] Ehresmann, C., Categories topologiques et categories differentiables, Coll. de Geom. Differ. Globale, Bruxelles (1959), 137-150.
Mathematical Reviews (MathSciNet):
MR116360
Zentralblatt MATH:
0205.28202
[6] Guillemin, V. and Sternberg, S., The moment map and collective motion, Ann. of Phys., 127 (1980), 220-253.
Mathematical Reviews (MathSciNet):
MR576424
Zentralblatt MATH:
0453.58015
[7] Karasev, M. V., Analogues of objects of Lie group theory for nonlinear Poisson brackets. Math. USSR Izv.3 28 (1987), 497-527.
Zentralblatt MATH:
0624.58007
[8] Kazhdan, D., Kostant, B. and Sternberg, S., Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure and Appl. Math., 31 (1978), 481-507.
Mathematical Reviews (MathSciNet):
MR478225
Zentralblatt MATH:
0368.58008
[9] Lie, S., Theorie der Transformationsgruppen, Zweiter Abschnitt unter Mitwurking von Prof. Dr. Friedrich Engel, Teubner, Leibzig, 1890.
Jahrbuch database (Zbl):
23.0364.01
[10] Marie, C.-M., Symplectic manifolds, dynamical groups, and Hamiltonian mechanics, Diff. Geometry and relativity, Reidel (1976), 243-269.
Mathematical Reviews (MathSciNet):
MR438393
Zentralblatt MATH:
0369.53042
[11] Marsden, J. and Ratiu, T., Reduction of Poisson manifolds, Lett in Math. Phys., 11 (1986), 161-169.
Mathematical Reviews (MathSciNet):
MR836071
Zentralblatt MATH:
0602.58016
[12] Marsden, J., Ratiu, T. and Weinstein, A., Semidirect products and reduction in mechanics, Trans. Amer. Math. Soc., 281 (1984), 147-177.
Mathematical Reviews (MathSciNet):
MR719663
Zentralblatt MATH:
0529.58011
[13] Marsden, J. and Weinstein, A., Reduction of symplectic manifolds with symmetry, Rep. Math. Phys., 5 (1974), 121-129.
Mathematical Reviews (MathSciNet):
MR402819
Zentralblatt MATH:
0327.58005
[14] Meyer, K. R., Symmetries and integrals in mechanics, in Dynamical Systems, M. M. Peixoto, ed., Academic Press, New York (1973), 259-272.
Mathematical Reviews (MathSciNet):
MR331427
Zentralblatt MATH:
0293.58009
[15] Renault, J., A groupoid approach to C*-algebras, Lecture Notes in Math., 793 (1980).
Mathematical Reviews (MathSciNet):
MR584266
Zentralblatt MATH:
0433.46049
[16] Semenov-Tian-Shansky, M. A., Dressing transformations and Poisson group actions, Publ. RIMS, Kyoto Univ., 21 (1985), 1237-1260.
Mathematical Reviews (MathSciNet):
MR842417
Zentralblatt MATH:
0674.58038
[17] Smale, S., Topology and mechanics. I, Invent. Math., 10 (1970), 305-331.
Mathematical Reviews (MathSciNet):
MR309153
Zentralblatt MATH:
0202.23201
[18] Weinstein, A., Lectures on symplectic manifolds, CBMS Regional Conf. Ser. in Math., 29 (1977).
Mathematical Reviews (MathSciNet):
MR464312
Zentralblatt MATH:
0406.53031
[19] Weinstein, A., The local structure of Poisson manifolds, J. Diff. Geom., 18 (1983), 523-557.
Mathematical Reviews (MathSciNet):
MR723816
Zentralblatt MATH:
0524.58011
[20] Weinstein, A., Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc., 16 (1987), 101-104.
Mathematical Reviews (MathSciNet):
MR866024
Zentralblatt MATH:
0618.58020
[21] Weinstein, A., Poisson geometry of the principal series and nonlinearizable structures, J. Diff. Geom., 25 (1987), 55-73.
Mathematical Reviews (MathSciNet):
MR873455
Zentralblatt MATH:
0592.58024
[22] Weinstein, A., Coisotropic calculus and Poisson groupoids, Subwitted to J. Math Soc Japan.
Mathematical Reviews (MathSciNet):
MR959095
Zentralblatt MATH:
0642.58025
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