切Poisson作用及约化  

Tangential Poisson Actions and Reductions

作　　者：杨奇林[1] 

机构地区：[1]中国科学院数学研究所

出　　处：《数学进展》2002年第2期127-134,共8页Advances in Mathematics（China）

基　　金：Post Doctorial Science Foundation of China.

摘　　要：本文证明了单连通Ｐｏｉｓｓｏｎ紧李群切作用及约化Ｐｏｉｓｓｏｎ作用于Ｐｏｉｓｓｏｎ流形，若带有等动量映射，则可通过调整Ｐｏｉｓｓｏｎ流形的Ｐｏｉｓｓｏｎ结构，变成保Ｐｏｉｓｓｏｎ结构的Ｐｏｉｓｓｏｎ作用，并且该作用限制到Ｐｏｉｓｓｏｎ流形的辛叶片上，相对于新Ｐｏｉｓｓｏｎ结构是Ｈａｍｉｌｔｉｏｎ作用．我们把Ｍｅｙｅｒ－Ｍａｒｓｄｅｎ－Ｗｅｉｎｓｔｅｉｎ约化从Ｈａｍｉｌｔｉｏｎ作用推广到切Ｐｏｉｓｓｏｎ作用，包括正则值和非正则值两种情形．We show that the tangential Poisson action of a connected compact simple Poisson- Lie group with an equivariant momentum map can be adjusted to be a Poisson structure preserved action, and, on the symplectic leaves of that Poisson manifold, the restricted actions are Hamiltonian with respect to the new Poisson structure. We also generalize the Meyer-Marsden-Weinstein reduction from Hamilton action to tangential Poisson action including both regular and non-regular cases.

关 键 词：动量映射 切Poisson作用 约化 李群 POISSON流形 

分 类 号：O187[理学—数学]