Automorphisms of Lie groupoids and symplectic reduction on orbifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910228856963072 |
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| author | Chen, Bohui Du, Cheng-Yong Jiang, Fengyu |
| author_facet | Chen, Bohui Du, Cheng-Yong Jiang, Fengyu |
| contents | 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 étale 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_17351 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automorphisms of Lie groupoids and symplectic reduction on orbifolds Chen, Bohui Du, Cheng-Yong Jiang, Fengyu Differential Geometry Symplectic Geometry 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 étale 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. |
| title | Automorphisms of Lie groupoids and symplectic reduction on orbifolds |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2605.17351 |