Dirac submanifolds and Poisson involutions
Ping Xu (2003)
Annales scientifiques de l'École Normale Supérieure
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Ping Xu (2003)
Annales scientifiques de l'École Normale Supérieure
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Nunes da Costa, J.M. (1997)
Portugaliae Mathematica
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Alan Weinstein (2000)
Banach Center Publications
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Manuel de León, David Martín de Diego (1995)
Extracta Mathematicae
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Veronique Chloup (2000)
Banach Center Publications
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The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.
Rybicki, Tomasz
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Author’s abstract: “We introduce the concept of the flux homomorphism for regular Poisson manifolds. First we establish a one-to-one correspondence between Poisson diffeomorphisms close to and closed foliated 1-forms close to 0. This allows to show that the group of Poisson automorphisms is locally contractible and to define the flux locally. Then, by means of the foliated cohomology, we extend this local homomorphism to a global one”.
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....