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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 $(G, \pi_G)$.
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Tangent and cotangent bundles: differential geometry
Yano, K., and Ishihara, S · 1973
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Reduction of symplectic manifolds with symmetry
Marsden, J. E., and Weinstein, A · 1974
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Hamiltonian systems, Lagrangian systems and the Legendre transformation
Tulczyjew, W. M · 1974
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Foundations of Mechanics
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Remarques sur les réductions symplectiques
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The category of symplectic reductions
Benenti, S · 1983
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Hamiltonian structures on Lie groups, Lie bialgebras, and the geometric meaning of the classical Yang-Baxter equations
Drinfeld, V · 1983
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Reduction and quantization for singular momentum mappings
Śniatycki, J., and Weinstein, A · 1983
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Reduction of Poisson manifolds
Marsden, J. E., and Ratiu, T · 1986
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Derivations of differential forms on jet bundles
Pidello, G., and Tulczyjew, W. M · 1987
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Moments and reduction for symplectic groupoids
Mikami, K., and Weinstein, A · 1988
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Coisotropic calculus and Poisson groupoids
Weinstein, A · 1988
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Multiplicative and Affine Poisson structure on Lie groups
Lu, J.-H · 1990
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Lu, J.-H · 1991
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Tangent lifts of Poisson and related structures
Grabowski, J., and Urbański, P · 1995
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Exact Gerstenhaber algebras and Lie bialgebroids
Kosmann-Schwarzbach, Y · 1995
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Xu, P · 1995
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Ginzburg, V. L · 1996
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Mackenzie, K. C. H · 2005
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An extension of the Marsden-Ratiu reduction for Poisson manifolds
Falceto, F., and Zambon, M · 2008
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Bursztyn, H., Iglesias Ponte, D., and Ševera, P · 2009
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Integrability of Poisson Lie group actions
Fernandes, R. L., and Iglesias Ponte, D · 2009
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The momentum map in Poisson geometry
Fernandes, R. L., Ortega, J.-P., and Ratiu, T. S · 2009
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Jotz, M., and Ratiu, T. S · 2009
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Cannas da Silva, A., and Weinstein, A · 1999
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A slow and careful Legendre transformation for singular Lagrangians
Tulczyjew, W. M., and Urbański, P · 1999
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BRST cohomology and phase space reduction in deformation quantization
Bordemann, M., Herbig, H., and Waldmann, S · 2000
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Lagrangian reduction by stages
Cendra, H., Marsden, J. E., and Ratiu, T. S · 2001
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Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
Cattaneo, A. S., and Felder, G · 2004
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Esposito, C., and Nest, R · 2012
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Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures
Marrero, J. C., Padrón, E., and Rodríguez-Olmos, M · 2012
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A supergeometric approach to Poisson reduction
Cattaneo, A. S., and Zambon, M · 2013
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Differential Geometry of Singular Spaces and Reduction of Symmetry
Śniatycki, J · 2013
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Poisson reduction
Esposito, C · 2014
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Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
García-Toraño Andrés, E., Guzmán, E., Marrero, J. C., and Mestdag, T · 2014
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