Reduction of pre-Hamiltonian actions

JOURNAL OF GEOMETRY AND PHYSICS

卷:115

Article

De Nicola, Antonio¹  Esposito, Chiara² 

[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

[2] Julius Maximilian Univ Wurzburg, Dept Math, Fac Math & Comp Sci, Chair Math X Math Phys, Wurzburg, Germany

关键词: Poisson-Lie groups;    Tangent bundle;    Reduction;    Lie algebroids;    Lie groupoids;    Tulczyjew isomorphism;   

DOI  :  10.1016/j.geomphys.2016.03.017

来源: Elsevier

【 摘 要 】

We prove a reduction theorem for the tangent bundle of a Poisson manifold (M, pi) endowed with a pre-Hamiltonian action of a Poisson Lie group (G, pi(G)). In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden Ratiu reduction of M. If the manifold M is symplectic and simply connected, the reduced tangent bundle is integrable and its integral symplectic groupoid is the Marsden Weinstein reduction of the pair groupoid M x (M) over bar. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free