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arXiv · 2605.17351

Automorphisms of Lie groupoids and symplectic reduction on orbifolds

Bohui Chen·Cheng-Yong Du·Fengyu Jiang
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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.

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Bohui Chen, Cheng-Yong Du, Fengyu Jiang. 2026-05-17. Automorphisms of Lie groupoids and symplectic reduction on orbifolds. https://arxiv.org/abs/2605.17351

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