An Explicit Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$

Dadi Ni; Kaichuan Qi

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arXiv · 2601.05183

An Explicit Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$

Dadi Ni·Kaichuan Qi

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Abstract

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 ${\rm H}^3_G(G,\mathbb Z)$.

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Dadi Ni, Kaichuan Qi. 2026-01-08. An Explicit Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$. https://arxiv.org/abs/2601.05183

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