Journal of Differential Geometry

Poisson 2-Groups

Zhuo Chen, Mathieu Stiçnon, and 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.

Article information

Source
J. Differential Geom., Volume 94, Number 2 (2013), 209-240.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1367438648

Digital Object Identifier
doi:10.4310/jdg/1367438648

Mathematical Reviews number (MathSciNet)
MR3080481

Zentralblatt MATH identifier
1271.22021

Citation

Chen, Zhuo; Stiçnon, Mathieu; Xu, Ping. Poisson 2-Groups. J. Differential Geom. 94 (2013), no. 2, 209--240. doi:10.4310/jdg/1367438648. https://projecteuclid.org/euclid.jdg/1367438648


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