We introduce a notion of Poisson bialgebra as an analogue of a Lie bialgebra of Drinfeld. Poisson bialgebras exhibit many familiar properties of Lie bialgebras. In particular, they can be constructed from a combination of the classical Yang-Baxter equation and the associative Yang-Baxter equation and there exists a natural Drinfeld classical double. Moreover, Poisson bialgebras are related to certain algebraic structures and they fit naturally into a framework to construct compatible Poisson brackets in integrable systems.
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Research Article| February 28 2013
Xiang Ni, Chengming Bai; Poisson bialgebras. J. Math. Phys. 1 February 2013; 54 (2): 023515. https://doi.org/10.1063/1.4792668
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