Zhuo Chen, Mathieu Stienon, Ping Xu
Published 2012-02-01, updated 2013-02-05Version 2
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.
Holonomy of supermanifolds
Noncompact homogeneous Einstein manifolds attached to graded Lie algebras
On complex-analytic $1|3$-dimensional supermanifolds associated with $\mathbb{CP}^1$
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