Geodesic
Poisson–Lie sigma models on Drinfel’d double
Archivum mathematicum, Tome 48 (2012) no. 5, pp. 423-447.

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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. Using the adjoint representation of Lie group and Drinfel’d double we show that Poisson-Lie group can be constructed for general Lie bialgebra.
DOI : 10.5817/AM2012-5-423
Classification : 53D17, 70G45
Keywords: Poisson sigma models; Poisson manifolds; Poisson-Lie groups; bundle maps 
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Vysoký, Jan; Hlavatý, Ladislav. Poisson–Lie sigma models on Drinfel’d double. Archivum mathematicum, Tome 48 (2012) no. 5, pp. 423-447. doi : 10.5817/AM2012-5-423. http://geodesic.mathdoc.fr/articles/10.5817/AM2012-5-423/

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