关于辛仿射群和群胚上的讨论

Discussion on Symplectic-Affine Group and Groupoids

由于李群H上的G-仿射群是一个李群,所以它具有李群的性质。文章根据辛李群的概念,定义了辛仿射群,并讨论了他的相关性质,文章最后分别证明了微分同胚保持Poisson群胚及辛群胚的Poisson结构和辛结构。

The G-Affine group on the Lie group H is a Lie group,so it has the characteristics of the Lie group. This paper, by considering the definition of Symplectic--Lie group, defines Symplectic--Affine group and discusses some of its charateristics, and finally proves respectively that the differential homeo-morphism keeps the Possion structure on the Possion--groupoids and Symplectic structure on the Symlectic--groupoids.