Poisson manifolds, Lie algebroids, modular classes: a survey.
Kosmann-Schwarzbach, Yvette (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Kosmann-Schwarzbach, Yvette (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Janusz Grabowski, Giuseppe Marmo, Peter W. Michor (2006)
Annales de l’institut Fourier
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For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.
Izu Vaisman (2000)
Annales Polonici Mathematici
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We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.
Yvette Kosmann-Schwarzbach, Franco Magri (1990)
Annales de l'I.H.P. Physique théorique
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Pantelis A. Damianou, Rui Loja Fernandes (2008)
Annales de l’institut Fourier
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It is well-known that the Poisson-Nijenhuis manifolds, introduced by Kosmann-Schwarzbach and Magri form the appropriate setting for studying many classical integrable hierarchies. In order to define the hierarchy, one usually specifies in addition to the Poisson-Nijenhuis manifold a bi-hamiltonian vector field. In this paper we show that to every Poisson-Nijenhuis manifold one can associate a canonical vector field (no extra choices are involved!) which under an appropriate assumption...
Popescu, Liviu (2009)
Balkan Journal of Geometry and its Applications (BJGA)
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Jan Vysoký, Ladislav Hlavatý (2012)
Archivum Mathematicum
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Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras....