Poisson 2-groups
Differential Geometry
2021-06-07 v2 High Energy Physics - Theory
Quantum Algebra
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.
Cite
@article{arxiv.1202.0079,
title = {Poisson 2-groups},
author = {Zhuo Chen and Mathieu Stienon and Ping Xu},
journal= {arXiv preprint arXiv:1202.0079},
year = {2021}
}
Comments
34 pages