An Explicit Construction of \mathbbS¹-Gerbes over the Stack [G/G]

2026/01/08 by Dadi Ni, Kaichuan Qi · 1 voice
Mathematics · #math.SG

paper · pdf

arxiv published 2026/01/08 · arxiv updated 2026/04/30

Abstract

For a compact and connected Lie group G, we present an explicit construction of an \mathbbS¹-gerbe over the differentiable stack [G/G] in the framework of \mathbbS¹-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 H³_G(G,\mathbb Z).

Citations

• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Groupoid equivariant prequantization
• The Atiyah algebroid of the path fibration over a Lie group
• G-gerbes, principal 2-group bundles and characteristic classes
• Differentiable Stacks and Gerbes
• General Theory of Lie Groupoids and Lie Algebroids
• Basic gerbe over non-simply connected compact groups
• Integration of twisted Dirac brackets
• Equivariant gerbes over compact simple Lie groups
• The basic gerbe over a compact simple Lie group
• WZW branes and gerbes
• Gerbes over Orbifolds and Twisted K-theory
• Gerbes over Orbifolds and Twisted K-Theory
• Integrability of Lie brackets
• Integrability of Lie brackets
• Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes
• Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes
• Lie Group Valued Moment Maps
• Higher bundle gerbes and cohomology classes in gauge theories
• Bundle gerbes
• Bundle Gerbes

Discussions

• Dadi Ni, Kaichuan Qi: Construction of $\mathbb{S}^1$-Gerbes over the Stack $[G/G]$ https://arxiv.org/abs/2601.05183 https://arxiv.org/pdf/2601.05183 https://arxiv.org/html/2601.05183 [bsky, 0 points, 0 comments]

Related

• Equivariant gerbes over compact simple Lie groups
• Differentiable Stacks and Gerbes
• S¹-bundles and gerbes over differentiable stacks
• Lie groupoids and crossed module-valued gerbes over stacks
• Gerbes and Lie Groups