Automorphisms of Lie groupoids and symplectic reduction on orbifolds
Differential Geometry
2026-05-19 v1 Symplectic Geometry
Abstract
In this paper, the 2-group BAut(X) of automorphisms of a Lie groupoid X is constructed. Considering the 2-group G action on X, we explain the equivalence between 2-group homomorphisms from G to BAut(X) with Kan fibrations over G with fiber X. This justifies the notion of Kan fibration for 2-group actions on Lie groupoids. As an application, we formulate Hamiltonian actions of \'etale Lie 2-groups on orbifolds in terms of Kan fibrations and study the symplectic reductions. We show that, in general, the reduction is in fact a symplectic Lie 2-groupoid, and under certain isotropic free condition, the reduction is still an orbifold. Also the slice theorem of a group G action on Lie groupoids is proved.
Keywords
Cite
@article{arxiv.2605.17351,
title = {Automorphisms of Lie groupoids and symplectic reduction on orbifolds},
author = {Bohui Chen and Cheng-Yong Du and Fengyu Jiang},
journal= {arXiv preprint arXiv:2605.17351},
year = {2026}
}