An Explicit Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909002607099904 |
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| author | Ni, Dadi Qi, Kaichuan |
| author_facet | Ni, Dadi Qi, Kaichuan |
| contents | For a compact and connected Lie group $G$, we present an explicit construction of an $\mathbb{S}^1$-gerbe over the differentiable stack $[G/G]$ in the framework of $\mathbb{S}^1$-central extensions of Lie groupoids. This gives a complete proof of the construction outlined earlier by Behrend--Xu--Zhang, together with an explicit proof of the differential-form identity stated there without proof. In particular, when $G$ is compact, simple, and simply connected, the Dixmier--Douady class of the resulting gerbe is the canonical generator of ${\rm H}^3_G(G,\mathbb Z)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05183 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Explicit Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$ Ni, Dadi Qi, Kaichuan Symplectic Geometry 53D17, 53D20, 22E67 For a compact and connected Lie group $G$, we present an explicit construction of an $\mathbb{S}^1$-gerbe over the differentiable stack $[G/G]$ in the framework of $\mathbb{S}^1$-central extensions of Lie groupoids. This gives a complete proof of the construction outlined earlier by Behrend--Xu--Zhang, together with an explicit proof of the differential-form identity stated there without proof. In particular, when $G$ is compact, simple, and simply connected, the Dixmier--Douady class of the resulting gerbe is the canonical generator of ${\rm H}^3_G(G,\mathbb Z)$. |
| title | An Explicit Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$ |
| topic | Symplectic Geometry 53D17, 53D20, 22E67 |
| url | https://arxiv.org/abs/2601.05183 |