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arXiv · 1202.0079

Poisson 2-groups

Zhuo Chen·Mathieu Stienon·Ping Xu
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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.

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Zhuo Chen, Mathieu Stienon, Ping Xu. 2012-02-01. Poisson 2-groups. https://doi.org/10.4310/jdg/1367438648

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