Integrability of Poisson-Lie Group Actions

被引：12

作者：

Fernandes, Rui Loja ^{[1
]}

Iglesias Ponte, David ^{[2
]}

机构：

[1] Univ Tecn Lisboa, Dept Matemat, Inst Super Tecn, P-1049001 Lisbon, Portugal

[2] CSIC, Inst Ciencias Matemat, UAM, UCM,UC3M, E-28006 Madrid, Spain

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2009年 / 90卷 / 1-3期

关键词：

Poisson actions; twisted multiplicative; integrability; HOMOGENEOUS SPACES; SYMPLECTIC GROUPOIDS; INTEGRATION; BRACKETS;

D O I：

10.1007/s11005-009-0348-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative Hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group G on a Poisson manifold M, we find an explicit description of the lifted Hamiltonian action on the symplectic groupoid I (M) pound. We give applications of these results to the integration of Poisson quotients M/G, Lu-Weinstein quotients mu(-1)(e)/G and Poisson homogeneous spaces G/H.

引用

页码：137 / 159

页数：23

共 20 条

[1]

Alekseev AY, 1997, J DIFFER GEOM, V45, P241

[2] On the integration of Poisson homogeneous spaces [J].

Bonechi, Francesco ;

Ciccoli, Nicola ;

Staffolani, Nicola ;

Tarlini, Marco .

JOURNAL OF GEOMETRY AND PHYSICS, 2008, 58 (11) :1519-1529

[3] Gauge equivalence of Dirac structures and symplectic groupoids [J].

Bursztyn, H ;

Radko, O .

ANNALES DE L INSTITUT FOURIER, 2003, 53 (01) :309-+

[4]

Crainic M, 2004, J DIFFER GEOM, V66, P71

[5] Integrability of Lie brackets [J].

Crainic, M ;

Fernandes, RL .

ANNALS OF MATHEMATICS, 2003, 157 (02) :575-620

[6] ON POISSON HOMOGENEOUS SPACES OF POISSON-LIE GROUPS [J].

DRINFELD, VG .

THEORETICAL AND MATHEMATICAL PHYSICS, 1993, 95 (02) :524-525

[7]

Ginzburg Viktor L., 1992, J AM MATH SOC, V5, P445, DOI [/10.2307/2152773, DOI 10.2307/2152773]

[8]

Lu J.-H., 1990, PhD thesis

[9] Poisson homogeneous spaces and Lie algebroids associated to Poisson actions [J].

Lu, JH .

DUKE MATHEMATICAL JOURNAL, 1997, 86 (02) :261-304

[10]

LU JH, 1991, MATH SCI R, V20, P209

← 1 2 →