Poisson-Nijenhuis structures

Yvette Kosmann-Schwarzbach; Franco Magri

Displaying similar documents to “Poisson-Nijenhuis structures”

Poisson–Lie sigma models on Drinfel’d double

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....

Drinfel'd doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids.

Mackenzie, K.C.H. (1998)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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General poisson algebras

Grabowski, Janusz

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On Riemann-Poisson Lie groups

Brahim Alioune, Mohamed Boucetta, Ahmed Sid’Ahmed Lessiad (2020)

Archivum Mathematicum

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A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [4]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.

Linearization and star products

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.