Abstract
We prove a 2-categorical analogue of a classical result of Drinfeld: there is a one-to-one correspondence between connected, simply connected Poisson Lie 2-groups and Lie 2-bialgebras. In fact, we also prove that there is a one-to-one correspondence between connected, simply connected quasi-Poisson 2-groups and quasi-Lie 2-bialgebras. Our approach relies on a “universal lifting theorem” for Lie 2-groups: an isomorphism between the graded Lie algebras of multiplicative polyvector fields on the Lie 2-group on one hand and of polydifferentials on the corresponding Lie 2-algebra on the other hand.
Citation
Zhuo Chen. Mathieu Stiçnon. Ping Xu. "Poisson 2-Groups." J. Differential Geom. 94 (2) 209 - 240, June 2013. https://doi.org/10.4310/jdg/1367438648
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