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arXiv · 1211.0901

Poisson-Lie Sigma Models on Drinfel'd double

Jan Vysoky·Ladislav Hlavaty
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Abstract

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.

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Jan Vysoky, Ladislav Hlavaty. 2012-11-05. Poisson-Lie Sigma Models on Drinfel'd double. https://doi.org/10.5817/am2012-5-423

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