2026/06/21 by Dadi Ni, Kaichuan Qi · 1 voice
Mathematics · #math.SG #math.DG
arxiv published 2026/06/21 · arxiv updated 2026/06/23
We study affine deformations of the cotangent groupoid T^*G \rightrightarrows A^*, governed by a one-form γ∈Ω1(\mathcal G(2)), and characterize the conditions on γ under which this construction is valid. We show that these deformations arise naturally from \mathbbS1-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 \mathbbS1-gerbes.