余切群胚的辛约化
Symplectic Reduction for Cotangent Groupoids
摘要: 给定李群胚以及I-空间N,本文考虑了余切群胚在余切丛TN上的辛群胚作用,并给出了辛约化的具体表示。
Abstract: Given a Lie groupoid  and I-space N, this paper considers symplectic groupoid actions of the cotangent groupoid  on the cotangent bundle TN. Meanwhile, this reduction is investigated concretely.
文章引用:戴远莉. 余切群胚的辛约化[J]. 理论数学, 2021, 11(3): 323-329. https://doi.org/10.12677/PM.2021.113043

参考文献

[1] Arnold, V. (1966) Sur la gèométrie diffèrentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits. Annales de l’Institut Fourier, 16, 319-361. [Google Scholar] [CrossRef
[2] Smale, S. (1970) Topology and Mechanics. I. Inventiones Mathematicae, 10, 305-331. [Google Scholar] [CrossRef
[3] Meyer, K.R. (1973) Symmetries and Integrals in Mathematics. Dy-namical Systems, Academic Press, New York, 259-272. [Google Scholar] [CrossRef
[4] Marsden, J. and Weinstein, A. (1974) Reduction of Symplectic Manifolds with Symmetry. Reports on Mathematical Physics, 5, 121-130. [Google Scholar] [CrossRef
[5] Marsden, J.E., Misiolek, G., Ortega, J.P., et al. (2007) Ham-iltonian Reduction by Stages. Springer, New York, 1-64.
[6] Mackenzie, K.C.H. (2005) General Theory of Lie Groupoids and Lie Algebroids. Cambridge University Press, New York. [Google Scholar] [CrossRef
[7] da Silva, A.C. (2008) Lectures on Symplectic Geometry. Springer, New York, 7-22. [Google Scholar] [CrossRef
[8] Mikami, K. and Weinstein, A. (1988) Moments and Reduction for Symplectic Groupoids. Publications of the Research Institute for Mathematical Sciences, 24, 121-140. [Google Scholar] [CrossRef