Poisson 2-groups

Zhuo Chen Tsinghua University Mathieu Stienon Pennsylvania State University Ping Xu Pennsylvania State University

Differential Geometry mathscidoc:1609.10313

Journal of Differential Geometry, 94, (2), 209-240, 2013
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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  title={POISSON 2-GROUPS},
  author={Zhuo Chen, Mathieu Stienon, and Ping Xu},
  booktitle={Journal of Differential Geometry},
Zhuo Chen, Mathieu Stienon, and Ping Xu. POISSON 2-GROUPS. 2013. Vol. 94. In Journal of Differential Geometry. pp.209-240. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914075608054587975.
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