Universal deformation formulae, symplectic lie groups and symmetric spaces

被引:18
作者
Bieliavsky, Pierre [1 ]
Bonneau, Philippe [2 ]
Maeda, Yoshiaki [3 ]
机构
[1] Univ Catholique Louvain, Dept Math, B-1348 Louvain, Belgium
[2] Univ Metz, CNRS, UMR 7122, Lab Math & Applicat Metz, F-57045 Metz 1, France
[3] Keio Univ, Fac Sci & Technol, Dept Math, Kohoku Ku, Yokohama, Kanagawa 2238522, Japan
关键词
universal deformation formula; symplectic Lie group; symmetric space; Lie group actions;
D O I
10.2140/pjm.2007.230.41
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We define a class of symplectic Lie groups associated with solvable symmetric spaces. We give a universal strict deformation formula for every proper action of such a group on a smooth manifold. We define a functional space where performing an asymptotic expansion of the nonformal deformed product in powers of the deformation parameter yields an associative formal star product on the symplectic Lie group at hand. The cochains of the star product are explicitly given ( without recursion) in the two-dimensional case of the affine group ax+b. The latter differs from the Giaquinto - Zhang construction, as shown by analyzing the invariance groups. In a Hopf algebra context, the above formal star product is shown to be a smash product and a compatible coproduct is constructed.
引用
收藏
页码:41 / 57
页数:17
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