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arXiv · 2606.22288

Affine deformations of cotangent groupoids

Dadi Ni·Kaichuan Qi
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Abstract

We study affine deformations of the cotangent groupoid $T^*\mathcal{G} \rightrightarrows A^*$, governed by a one-form $\gamma\in\Omega^1(\mathcal G^{(2)})$, and characterize the conditions on $\gamma$ under which this construction is valid. We show that these deformations arise naturally from $\mathbb{S}^1$-central extensions of Lie groupoids via symplectic reduction, and identify the reduced symplectic form as a multiplicative magnetic form. In particular, for Kac-Moody extensions, this construction yields nontrivial deformations of quotient stacks and $\mathbb{S}^1$-gerbes.

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Dadi Ni, Kaichuan Qi. 2026-06-21. Affine deformations of cotangent groupoids. https://arxiv.org/abs/2606.22288

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