G匚W上的泊松群胚结构The Poisson groupoids structure on G匚W
袁丽霞;王宝勤;卢维娜;
摘要(Abstract)：
从泊松作用的角度考察了群胚上的半直积结构,定义了泊松群胚对泊松群胚的泊松作用,讨论了其性质,并证明了两个泊松群胚的半直积仍是泊松群胚,从而对群胚的半直积结构有了更多的认识.
关键词(KeyWords)： 泊松群胚;泊松群胚作用;半直积
基金项目(Foundation): 新疆师范大学优秀青年教师科研启动基金(XJNU0728)
作者(Authors): 袁丽霞;王宝勤;卢维娜;
参考文献(References)：
- [1]Mackenzie K C H.Lie Groupoids and Lie Algebroids in Differential Geometry[M].Cambridge:CambridgeUniversity Press,1987.
- [2]王宝勤,袁丽霞,赵晓华.关于李群胚和泊松作用的讨论[J].纯粹数学和应用数学,2007,23(4):487-492.
- [3]Mackenzie K C H.General Theory of Lie Groupoids and Lie Algebroids[M].Cambridge:Cambridge Universitypress,2005.
- [4]王宝勤,袁丽霞,侯传燕.Several discussions on Lie groupoids[J].应用数学,2006,19(4):731-736.
- [5]Liu Z J,Weinstein A,Xu Pin.Dirac structures and Poisson homogeneous spaces[J].Commun.Math.Phys.,1998,192:121-144.
- [6]Liu Baokang.Some properties on product poisson manifolds[J].J.Capital Nor.Univ.,1999,3(20):21-25.
- [7]Xu P.On Poisson groupoids[J].Int.J.Math.,1995,6(1):101-124.
- [8]Chen Z,Liu Z J.On transitive Lie bialgebroids and Poisson groupoids[J].Diff.Geom.Appl.,2005,22:253-274.
- [9]Weistein A.Poisson geometry[J].Diff.Geom.Appl.,1998,9:213-238.
- [10]Liu Z J.Some remarks on dirac structures and poisson reductions[J].Banach Center Publ.,2000,51:165-173.
- [11]Mackenzie K C H,Xu P.Lie bialgebroids and poisson groupoids[J].Duke Math.,1994,18:415-452.
- [12]袁丽霞,王宝勤.Induced connections of associated groupoids[J].数学进展,2008,37(5):617-624.