AFFINE GROUP AS SYMPLECTIC MANIFOLD

被引：16

作者：

BORDEMANN, M

MEDINA, A

OUADFEL, A

机构：

[1] UNIV DAVIGNON,DEPT MATH,CNRS,UA 1407,F-84000 AVIGNON,FRANCE

[2] UNIV MONTPELLIER 2,DEPT MATHEMAT,F-34095 MONTPELLIER 5,FRANCE

来源：

TOHOKU MATHEMATICAL JOURNAL | 1993年 / 45卷 / 03期

关键词：

LEFT INVARIANT SYMPLECTIC FORMS; LEFT INVARIANT FOLIATIONS; AFFINE GROUP; EXACT SYMPLECTIC EMBEDDING;

D O I：

10.2748/tmj/1178225893

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a Lie group carrying a left invariant symplectic form certain Lagrangian foliations are considered. We describe all left invariant (exact) symplectic structures on the affine group K(n) x GL(K(n)) for K=R or C. It is shown that for some of these structures there exists an exact symplectic embeding of the real affine group onto an open subset of the cotangent bundle of the Euclidean group R(n) x SO(n).

引用

页码：423 / 436

页数：14

共 12 条

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ABRAHAM R, 1978, F MECHANICS

[2]

BABELON O, 1989, INTEGRABLE MODELS 1

[3] GENERALIZED LAX PAIRS, THE MODIFIED CLASSICAL YANG-BAXTER EQUATION, AND AFFINE GEOMETRY OF LIE-GROUPS [J].