期刊文献+

ON THE SYMPLECTIC REDUCTIONS 被引量:1

ON THE SYMPLECTIC REDUCTIONS
原文传递
导出
摘要 A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using tie existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results. A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第3期425-434,共10页 数学年刊(B辑英文版)
关键词 辛约化 动量映射 辛作用 Poisson作用 子群 辛流形 Poisson-Lie群 Hamilton作用 Symplectic reduction, Symplectic action, Poisson action, Momentum mapping, Stable subgroup
  • 相关文献

参考文献8

  • 1Abrahain,R.& Marsden,J.E.,Foundations of mechanics [M],2nd ed.Benjamin/Cummings,New York,1978.
  • 2Marsden.J.& Weinstin,A.,Reduction of symplectic manifolds with symmetry [J],Rep.Math.Phys.,5(1974),121 130.
  • 3Lu,J.H.,Momentum mappings and reduction of Poisson actions,Symplectic geometry,groupoid,and integrable systems [A],Séminaire sud-Rhodanien de géomélrie à Berkley (1989) [M],P.Dazord and A.Weinstein,eds.,Springer MSRI Series (1991),209-226.
  • 4Weistein,A.,The local structure of Poisson manifolds [J],J.Diff.Geometry,18(1983),523-557.
  • 5Lu,J.H.& Weistein,A.,Poisson Lie groups,dressing transformations,and Bruhat decompositions [J],J.Diff.Geomerty,31(1990),501-526.
  • 6Bourbaki,N.,Groupes et algébres de lie [M],Chapitres 2 et 3,Hermann,Paris,1972.
  • 7Semenov-Tian-Shansky,M.A.,Dressing transformations and Poisson group actions [J],Publ.RIMS,Kyoto University,21(1985),1237 1260.
  • 8Weinstcin,A.,Coisotropic calculus and Poisson groupoids [J],J.Math.Soc.Japan,40:4(1988),705-727.

同被引文献1

引证文献1

二级引证文献2

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部