1202.0079 (Zhuo Chen et al.)

Poisson 2-groups    [PDF]

Zhuo Chen, Mathieu Stienon, Ping Xu

We prove a 2-categorical analogue of a 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.

View original: http://arxiv.org/abs/1202.0079