李群的余伴随表示在泊松几何学中的应用

APPLICATIONS OF THE CO-ADJOINT REPRESENTATIONS OF LIE GROUPS IN POISSON GEOMETRY

本文研究了李群的余伴随表示.利用余伴随表示及等变的性质,获得了哈米顿系统中哈米顿函数及约化空间的结果,推广了哈米顿系统从而为约化问题的相关理论研究提供了必备的依据.

In this paper, we study the co-adjoint representations of Lie groups. By using the properties of the co-adjoint representations and equivariant, we have the results of Hamiltonian function and the reduced space in the Hamiltonian system, which generalizes the Hamiltonian system and provides the necessary foundation for the study of the reduced problems.