Lie bialgebroids and Poisson groupoids

@article{Mackenzie1994LieBA,
  title={Lie bialgebroids and Poisson groupoids},
  author={Kirill C. H. Mackenzie and Ping Xu},
  journal={Duke Mathematical Journal},
  year={1994},
  volume={73},
  pages={415-452}
}
Lie bialgebras arise as infinitesimal invariants of Poisson Lie groups. A Lie bialgebra is a Lie algebra g with a Lie algebra structure on the dual g∗ which is compatible with the Lie algebra g in a certain sense. For a Poisson group G, the multiplicative Poisson structure π induces a Lie algebra structure on the Lie algebra dual g∗ which makes (g, g∗) into a Lie bialgebra. In fact, there is a one-one correspondence between Poisson Lie groups and Lie bialgebras if the Lie groups are assumed to… 

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