Add to ORKGAbstract: We prove a reduction theorem for the tangent bundle of a Poisson manifold (M,π) endowed with a pre-Hamiltonian action of a Poisson Lie group (G,πG). 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 × M ̄. 1
This work introduces a unified approach to the reduction of Poisson manifolds using their descriptio...
As is well-known, there is a variational principle for theEuler–Poincar ́e equations on a Lie algebr...
This paper develops a reduction theory for Dirac structures that includes in a unified way, reductio...
We prove a reduction theorem for the tangent bundle of a Poisson manifold (M,π) endowed with a pre-H...
Abstract. Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian actio...
Abstract. The conditions under which it is possible to reduce a Poisson manifold via a regular folia...
31 pages, 14 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/This...
Extending our reduction construction in (S. Hu, Hamiltonian symmetries and reduction in generalized ...
8 pages.During the last thirty years, symplectic or Marsden--Weinstein reduction has been a major to...
This thesis concerns the study of Hamiltonian actions and momentum maps in the Poisson geometric fra...
A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group ...
Reduction in the category of Poisson manifolds is defined and some basic properties are derived. Th...
37 pagesThere exist three main approaches to reduction associated to canonical Lie group actions on ...
We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson ...
42 pagesWe generalize various symplectic reduction techniques to the context of the optimal momentum...
This work introduces a unified approach to the reduction of Poisson manifolds using their descriptio...
As is well-known, there is a variational principle for theEuler–Poincar ́e equations on a Lie algebr...
This paper develops a reduction theory for Dirac structures that includes in a unified way, reductio...
We prove a reduction theorem for the tangent bundle of a Poisson manifold (M,π) endowed with a pre-H...
Abstract. Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian actio...
Abstract. The conditions under which it is possible to reduce a Poisson manifold via a regular folia...
31 pages, 14 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/This...
Extending our reduction construction in (S. Hu, Hamiltonian symmetries and reduction in generalized ...
8 pages.During the last thirty years, symplectic or Marsden--Weinstein reduction has been a major to...
This thesis concerns the study of Hamiltonian actions and momentum maps in the Poisson geometric fra...
A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group ...
Reduction in the category of Poisson manifolds is defined and some basic properties are derived. Th...
37 pagesThere exist three main approaches to reduction associated to canonical Lie group actions on ...
We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson ...
42 pagesWe generalize various symplectic reduction techniques to the context of the optimal momentum...
This work introduces a unified approach to the reduction of Poisson manifolds using their descriptio...
As is well-known, there is a variational principle for theEuler–Poincar ́e equations on a Lie algebr...
This paper develops a reduction theory for Dirac structures that includes in a unified way, reductio...